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In [[mathematics]] a '''single-entry matrix''' is a [[matrix (mathematics)|matrix]] where a single element is one and the rest of the elements are zero,<ref>{{Cite web | |||
| author = Kaare Brandt Petersen & Michael Syskind Pedersen | |||
| title = The Matrix Cookbook | |||
| date = 2008-02-16 | |||
| url = http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3274/pdf/imm3274.pdf | |||
}}</ref><ref>{{Cite journal | |||
| author = Shohei Shimizu, Patrick O. Hoyer, Aapo Hyvärinen & Antti Kerminen | |||
| title = A Linear Non-Gaussian Acyclic Model for Causal Discovery | |||
| journal = [[Journal of Machine Learning Research]] | |||
| volume = 7 | |||
| year = 2006 | |||
| pages = 2003–2030 | |||
| url = http://www.cs.helsinki.fi/group/neuroinf/lingam/JMLR06.pdf | |||
}}</ref> e.g., | |||
:<math>\mathbf{J}^{23} = \left[\begin{matrix} | |||
0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{matrix}\right].</math> | |||
It is a specific type of a [[sparse matrix]]. | |||
The single-entry matrix can be regarded a row-selector when it is multiplied on the left side of the matrix, e.g.: | |||
: <math> | |||
\mathbf{J}^{23}\mathbf{A} = \left[ \begin{matrix} 0 & 0& 0 \\ a_{31} & a_{32} & a_{33} \\ 0 & 0 & 0 \end{matrix}\right] | |||
</math> | |||
Alternatively, a column-selector when multiplied on the right side: | |||
: <math> | |||
\mathbf{A}\mathbf{J}^{23} = \left[ \begin{matrix} 0 & 0 & a_{12} \\ 0 & 0 & a_{22} \\ 0 & 0 & a_{32} \end{matrix}\right] | |||
</math> | |||
The name, single-entry matrix, is not common, but seen in a few works.<ref>Examples: | |||
* {{cite web | |||
| title = Distributed Gain Matrix Optimization in | |||
Non-Regenerative MIMO Relay Networks | |||
| url = http://www.nari.ee.ethz.ch/wireless/pubs/files/asilomar09r.pdf | |||
}} | |||
* {{Cite web | |||
| author = Marcel Blattner | |||
| title = B-Rank: A top N Recommendation Algorithm | |||
| url = http://arxiv.org/pdf/0908.2741.pdf | |||
}}</ref> | |||
==References== | |||
{{Reflist}} | |||
{{DEFAULTSORT:Single-Entry Matrix}} | |||
[[Category:Sparse matrices]] | |||
{{Linear-algebra-stub}} | |||
Revision as of 22:11, 25 November 2013
In mathematics a single-entry matrix is a matrix where a single element is one and the rest of the elements are zero,[1][2] e.g.,
It is a specific type of a sparse matrix. The single-entry matrix can be regarded a row-selector when it is multiplied on the left side of the matrix, e.g.:
Alternatively, a column-selector when multiplied on the right side:
The name, single-entry matrix, is not common, but seen in a few works.[3]
References
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- ↑ Template:Cite web
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