Mathematical fallacy: Difference between revisions
Jump to navigation
Jump to search
en>Slawekb Revert not an example of division by zero, and tge subsequent text now makes no sense. Undid revision 507204788 by 117.216.124.67 (talk) |
en>BG19bot m WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9876) |
||
| Line 1: | Line 1: | ||
{{for|an introduction to the nature and significance of tensors in a broad context|Tensor}} | |||
In [[mathematics]], the modern [[component-free]] approach to the theory of a '''tensor''' views a tensor as an [[abstract object]], expressing some definite type of multi-linear concept. Their well-known properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extension of [[linear algebra]] to [[multilinear algebra]]. | |||
In [[differential geometry]] an intrinsic geometric statement may be described by a [[tensor field]] on a [[manifold]], and then doesn't need to make reference to coordinates at all. The same is true in [[general relativity]], of tensor fields describing a [[physical property]]. The component-free approach is also used heavily in [[abstract algebra]] and [[homological algebra]], where tensors arise naturally. | |||
:'''''Note:''' This article assumes an understanding of the [[tensor product]] of [[vector space]]s without chosen [[Basis (linear algebra)|bases]]. An overview of the subject can be found in the main [[tensor]] article. | |||
==Definition via tensor products of vector spaces== | |||
Given a finite set { ''V''<sub>1</sub>, ..., ''V''<sub>''n''</sub> } of [[vector space]]s over a common [[Field (mathematics)|field]] ''F'', one may form their [[Tensor product#Tensor product of vector spaces|tensor product]] ''V''<sub>1</sub> ⊗ ... ⊗ ''V''<sub>n</sub>, an element of which is termed a '''tensor'''. | |||
A '''tensor on the vector space''' ''V'' is then defined to be an element of (i.e., a vector in) a vector space of the form: | |||
:<math>V \otimes \cdots \otimes V \otimes V^* \otimes \cdots \otimes V^*</math> | |||
where ''V''* is the [[dual space]] of ''V''. | |||
If there are ''m'' copies of ''V'' and ''n'' copies of ''V''* in our product, the tensor is said to be of '''type (''m'', ''n'')''' and contravariant of order ''m'' and covariant order ''n'' and total [[tensor order|order]] ''m''+''n''. The tensors of order zero are just the scalars (elements of the field ''F''), those of contravariant order 1 are the vectors in ''V'', and those of covariant order 1 are the [[linear functional|one-forms]] in ''V''* (for this reason the last two spaces are often called the contravariant and covariant vectors). The space of all tensors of type (''m'',''n'') is denoted | |||
:<math> T^m_n(V) = \underbrace{ V\otimes \dots \otimes V}_{m} \otimes \underbrace{ V^*\otimes \dots \otimes V^*}_{n} .</math> | |||
The (1,1) tensors | |||
:<math>V \otimes V^*</math> | |||
are isomorphic in a natural way to the space of [[linear transformations]] from ''V'' to ''V''. A [[bilinear form]] on a real vector space ''V''; ''V'' × ''V'' → '''R''' corresponds in a natural way to a (0,2) tensor in | |||
:<math>V^* \otimes V^*</math> | |||
termed the associated ''[[metric tensor]]'' (or sometimes misleadingly the ''[[metric (mathematics)|metric]]'' or ''[[inner product]]'') and usually denoted '''''g'''''. | |||
==Tensor rank== | |||
The term '''rank of a tensor''' extends the notion of the [[rank of a matrix]] in linear algebra, although the term is also often used to mean the order (or degree) of a tensor. The rank of a matrix is the minimum number of column vectors needed to span the range of the matrix. A matrix thus has rank one if it can be written as an [[outer product]] of two nonzero vectors: | |||
:<math> A = v w^{\mathrm{T}}. </math> | |||
More generally, the rank of a matrix ''A'' is the smallest number of such outer products that can be summed to produce it: | |||
:<math>A = v_1w_1^\mathrm{T} + \cdots + v_kw_k^\mathrm{T}.</math> | |||
Similarly, a tensor of rank one (also called a '''simple tensor''') is a tensor that can be written as a tensor product of the form | |||
:<math>T=a\otimes b\otimes\cdots\otimes d</math> | |||
where ''a'', ''b'', ..., ''d'' are nonzero and in ''V'' or ''V''*. That is, if the tensor is nonzero and completely [[factorization|factorizable]]. In indices, a tensor of rank 1 is a tensor of the form | |||
:<math>T_{ij\dots}^{k\ell\dots}=a_ib_j\cdots c^kd^\ell\cdots.</math> | |||
Every tensor can be expressed as a sum of rank 1 tensors. The rank of a general tensor ''T'' is defined to be the minimum number of rank 1 tensors with which it is possible to express ''T'' as a sum {{harv|Bourbaki|1988|loc=II, §7, no. 8}}. | |||
A nonzero order 1 tensor always has rank 1. The [[zero tensor]] has rank zero. The rank of a tensor of order 2 agrees with the rank when the tensor is regarded as a [[Matrix (mathematics)|matrix]] {{harv|Halmos|1974|loc=§51}}, and can be determined from [[Gaussian elimination]] for instance. The rank of an order 3 or higher tensor is however often ''very hard'' to determine, and low rank decompositions of tensors are sometimes of great practical interest {{harv|de Groote|1987}}. Computational tasks such as the efficient multiplication of matrices and the efficient evaluation of polynomials can be recast as the problem of simultaneously evaluating a set of [[bilinear form]]s | |||
:<math>z_k = \sum_{ij} T_{ijk}x_iy_j\,</math> | |||
for given inputs ''x''<sub>''i''</sub> and ''y''<sub>''j''</sub>. If a low-rank decomposition of the tensor ''T'' is known, then an efficient [[evaluation strategy]] is known {{harv|Knuth|1998|pp=506–508}}. | |||
==Universal property== | |||
The space <math>T^m_n(V)</math> can be characterized by a [[universal property]] in terms of [[multilinear map]]pings. Amongst the advantages of this approach are that it gives a way to show that many linear mappings are "natural" or "geometric" (in other words are independent of any choice of basis). Explicit computational information can then be written down using bases, and this order of priorities can be more convenient than proving a formula gives rise to a natural mapping. Another aspect is that tensor products are not used only for [[free module]]s, and the "universal" approach carries over more easily to more general situations. | |||
A scalar-valued function on a [[Cartesian product]] (or [[Direct sum of modules|direct sum]]) of vector spaces | |||
:<math>f : V_1\times V_2\times\cdots\times V_N \to \mathbf{R}</math> | |||
is multilinear if it is linear in each argument. The space of all multlinear mappings from the product ''V''<sub>1</sub>×''V''<sub>2</sub>×...×''V''<sub>''N''</sub> into ''W'' is denoted | |||
''L''<sup>''N''</sup>(''V''<sub>1</sub>,''V''<sub>2</sub>,...,''V''<sub>''N''</sub>; ''W''). When ''N'' = 1, a multilinear mapping is just an ordinary linear mapping, and the space of all linear mappings from ''V'' to ''W'' is denoted ''L''(''V'';''W''). | |||
The [[tensor product#Characterization by a universal property|universal characterization of the tensor product]] implies that, for each multilinear function | |||
:<math>f\in L^{m+n}(\underbrace{V,V,\dots,V}_m,\underbrace{V^*,V^*,\dots,V^*}_n;W)</math> | |||
there exists a unique linear function | |||
:<math>T_f \in L(V\otimes\cdots\otimes V\otimes V^*\otimes\cdots\otimes V^*; W)</math> | |||
such that | |||
:<math>f(v_1,\dots,v_m,\alpha_1,\dots,\alpha_n) = T_f(v_1\otimes\cdots\otimes v_m\otimes\alpha_1\otimes\cdots\otimes\alpha_n)</math> | |||
for all ''v''<sub>''i''</sub> ∈ ''V'' and α<sub>''i''</sub> ∈ ''V''<sup>∗</sup>. | |||
Using the universal property, it follows that the space of (''m'',''n'')-tensors admits a [[natural isomorphism]] | |||
:<math>T^m_n(V) \cong | |||
L(V^* \otimes \dots \otimes V^* \otimes V \otimes \dots \otimes V ; \mathbb{R}) | |||
\cong L^{m+n}(V^*,\dots,V^*,V,\dots,V;\mathbb{R}).</math> | |||
In the formula above, the roles of ''V'' and ''V''<sup>*</sup> are reversed. In particular, one has | |||
:<math>T^1_0(V) \cong L(V^*;\mathbb{R}) \cong V</math> | |||
and | |||
:<math>T^0_1(V) \cong L(V;\mathbb{R}) = V^*</math> | |||
and | |||
:<math>T^1_1(V) \cong L(V;V).</math> | |||
==Tensor fields== | |||
{{Main|tensor field}} | |||
[[Differential geometry]], [[physics]] and [[engineering]] must often deal with [[tensor field]]s on [[smooth manifold]]s. The term ''tensor'' is sometimes used as a shorthand for ''tensor field''. A tensor field expresses the concept of a tensor that varies from point to point. | |||
==References== | |||
* {{Citation | |||
| last=Abraham | |||
| first=Ralph | |||
| author-link=Ralph Abraham | |||
| last2=Marsden | |||
| first2=Jerrold E. | |||
| author2-link=Jerrold E. Marsden | |||
| title=Foundations of Mechanics | |||
| edition=2 | |||
| year=1985 | |||
| publisher=Addison-Wesley | |||
| location=Reading, Mass. | |||
| isbn=0-201-40840-6 | |||
}}. | |||
* {{citation|first = Nicolas|last=Bourbaki|authorlink=Nicolas Bourbaki | title = Elements of mathematics, Algebra I| publisher = Springer-Verlag | year = 1989|isbn=3-540-64243-9}}. | |||
*{{citation | last = de Groote | first = H. F. | title = Lectures on the Complexity of Bilinear Problems | series= Lecture Notes in Computer Science | volume=245 | publisher = Springer | year = 1987 | isbn = 3-540-17205-X}}. | |||
* {{citation|authorlink=Paul Halmos|first=Paul|last=Halmos|title=Finite-dimensional Vector Spaces|year=1974|publisher=Springer|isbn=0-387-90093-4}}. | |||
*{{Citation | last1=Jeevanjee | first1=Nadir |year=2011 | title= An Introduction to Tensors and Group Theory for Physicists |url = http://www.springer.com/new+%26+forthcoming+titles+(default)/book/978-0-8176-4714-8 | isbn=978-0-8176-4714-8 }} | |||
*{{Citation | last1=Knuth | first1=Donald | author1-link=Donald Knuth | title=The Art of Computer Programming vol. 2 | origyear=1969 | edition=3rd | isbn=978-0-201-89684-8 | year=1998 | pages=145–146}}. | |||
{{tensors}} | |||
{{DEFAULTSORT:Tensor (Intrinsic Definition)}} | |||
[[Category:Tensors]] | |||
Revision as of 07:15, 23 January 2014
28 year-old Painting Investments Worker Truman from Regina, usually spends time with pastimes for instance interior design, property developers in new launch ec Singapore and writing. Last month just traveled to City of the Renaissance.
In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multi-linear concept. Their well-known properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extension of linear algebra to multilinear algebra.
In differential geometry an intrinsic geometric statement may be described by a tensor field on a manifold, and then doesn't need to make reference to coordinates at all. The same is true in general relativity, of tensor fields describing a physical property. The component-free approach is also used heavily in abstract algebra and homological algebra, where tensors arise naturally.
- Note: This article assumes an understanding of the tensor product of vector spaces without chosen bases. An overview of the subject can be found in the main tensor article.
Definition via tensor products of vector spaces
Given a finite set { V1, ..., Vn } of vector spaces over a common field F, one may form their tensor product V1 ⊗ ... ⊗ Vn, an element of which is termed a tensor.
A tensor on the vector space V is then defined to be an element of (i.e., a vector in) a vector space of the form:
where V* is the dual space of V.
If there are m copies of V and n copies of V* in our product, the tensor is said to be of type (m, n) and contravariant of order m and covariant order n and total order m+n. The tensors of order zero are just the scalars (elements of the field F), those of contravariant order 1 are the vectors in V, and those of covariant order 1 are the one-forms in V* (for this reason the last two spaces are often called the contravariant and covariant vectors). The space of all tensors of type (m,n) is denoted
The (1,1) tensors
are isomorphic in a natural way to the space of linear transformations from V to V. A bilinear form on a real vector space V; V × V → R corresponds in a natural way to a (0,2) tensor in
termed the associated metric tensor (or sometimes misleadingly the metric or inner product) and usually denoted g.
Tensor rank
The term rank of a tensor extends the notion of the rank of a matrix in linear algebra, although the term is also often used to mean the order (or degree) of a tensor. The rank of a matrix is the minimum number of column vectors needed to span the range of the matrix. A matrix thus has rank one if it can be written as an outer product of two nonzero vectors:
More generally, the rank of a matrix A is the smallest number of such outer products that can be summed to produce it:
Similarly, a tensor of rank one (also called a simple tensor) is a tensor that can be written as a tensor product of the form
where a, b, ..., d are nonzero and in V or V*. That is, if the tensor is nonzero and completely factorizable. In indices, a tensor of rank 1 is a tensor of the form
Every tensor can be expressed as a sum of rank 1 tensors. The rank of a general tensor T is defined to be the minimum number of rank 1 tensors with which it is possible to express T as a sum Template:Harv.
A nonzero order 1 tensor always has rank 1. The zero tensor has rank zero. The rank of a tensor of order 2 agrees with the rank when the tensor is regarded as a matrix Template:Harv, and can be determined from Gaussian elimination for instance. The rank of an order 3 or higher tensor is however often very hard to determine, and low rank decompositions of tensors are sometimes of great practical interest Template:Harv. Computational tasks such as the efficient multiplication of matrices and the efficient evaluation of polynomials can be recast as the problem of simultaneously evaluating a set of bilinear forms
for given inputs xi and yj. If a low-rank decomposition of the tensor T is known, then an efficient evaluation strategy is known Template:Harv.
Universal property
The space can be characterized by a universal property in terms of multilinear mappings. Amongst the advantages of this approach are that it gives a way to show that many linear mappings are "natural" or "geometric" (in other words are independent of any choice of basis). Explicit computational information can then be written down using bases, and this order of priorities can be more convenient than proving a formula gives rise to a natural mapping. Another aspect is that tensor products are not used only for free modules, and the "universal" approach carries over more easily to more general situations.
A scalar-valued function on a Cartesian product (or direct sum) of vector spaces
is multilinear if it is linear in each argument. The space of all multlinear mappings from the product V1×V2×...×VN into W is denoted LN(V1,V2,...,VN; W). When N = 1, a multilinear mapping is just an ordinary linear mapping, and the space of all linear mappings from V to W is denoted L(V;W).
The universal characterization of the tensor product implies that, for each multilinear function
there exists a unique linear function
such that
for all vi ∈ V and αi ∈ V∗.
Using the universal property, it follows that the space of (m,n)-tensors admits a natural isomorphism
In the formula above, the roles of V and V* are reversed. In particular, one has
and
and
Tensor fields
Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.
Differential geometry, physics and engineering must often deal with tensor fields on smooth manifolds. The term tensor is sometimes used as a shorthand for tensor field. A tensor field expresses the concept of a tensor that varies from point to point.
References
- Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010 - Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.