en>Mark viking: Noted interpretation and added a ref

2013-09-25T00:53:35Z

Noted interpretation and added a ref

← Older revision		Revision as of 02:53, 25 September 2013
Line 1:		Line 1:
	~~Nice to satisfy you~~, ~~my name is Refugia. For many years he~~'~~s been working as a meter reader~~ and it'~~s something he really enjoy. Minnesota has usually been his home but his spouse wants them to transfer. What I adore doing~~ is ~~to collect badges but I~~'~~ve been taking on new things recently.~~<br><br>~~Look at my blog post~~ :: [http://www.~~buzzbit~~.~~net~~/~~blog~~/~~288042 buzzbit~~.~~net~~]		In [[physics]] and [[mathematics]], the '''Golden–Thompson inequality''', proved independently by {{harvtxt\|Golden\|1965}} and {{harvtxt\|Thompson\|1965}}, says that for [[Hermitian matrix\|Hermitian matrices]] ''A'' and ''B'',

			:<math> \operatorname{tr}\, e^{A+B} \le \operatorname{tr} \left(e^A e^B\right)
			</math>

			where tr is the [[trace (linear algebra)\|trace]], and ''e''<sup>''A''</sup> is the [[matrix exponential]]. The inequality is of particular use in [[statistical mechanics]], and was first derived in that context.

			{{harvs\|txt\|first=Bertram\|last=Kostant\|year=1973\|authorlink=Bertram Kostant}} used the [[Kostant convexity theorem]] to generalize the Golden–Thompson inequality to all compact Lie groups.

			==References==

			*{{Citation \| last1=Bhatia \| first1=Rajendra \| title=Matrix analysis \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Graduate Texts in Mathematics \| isbn=978-0-387-94846-1 \| id={{MathSciNet \| id = 1477662}} \| year=1997 \| volume=169}}
			* J.E. Cohen, S. Friedland, T. Kato, F. Kelly, ''Eigenvalue inequalities for products of matrix exponentials'', Linear algebra and its applications, Vol. 45, pp. 55–95, 1982. {{doi\|10.1016/0024-3795(82)90211-7}}
			*{{Citation \| last1=Golden \| first1=Sidney \| title=Lower bounds for the Helmholtz function \| url=http://link.aps.org/doi/10.1103/PhysRev.137.B1127 \| doi= 10.1103/PhysRev.137.B1127 \| id={{MathSciNet \| id = 0189691}} \| year=1965 \| journal=Phys. Rev. \| series = Series II \| volume=137 \| pages=B1127–B1128}}
			*{{Citation \| last1=Kostant \| first1=Bertram \| title=On convexity, the Weyl group and the Iwasawa decomposition \| url= http://www.numdam.org/item?id=ASENS_1973_4_6_4_413_0 \| id={{MR\|0364552}} \| year=1973 \| journal=Annales Scientifiques de l'École Normale Supérieure. Quatrième Série \| issn=0012-9593 \| volume=6 \| pages=413–455}}
			* D. Petz, [http://www.renyi.hu/%7Epetz/pdf/64.pdf A survey of trace inequalities], in Functional Analysis and Operator Theory, 287–298, Banach Center Publications, 30 (Warszawa 1994).
			*{{Citation \| last1=Thompson \| first1=Colin J. \| title=Inequality with applications in statistical mechanics \| url=http://jmp.aip.org/jmapaq/v6/i11/p1812_s1 \| doi=10.1063/1.1704727 \| id={{MathSciNet \| id = 0189688}} \| year=1965 \| journal=[[Journal of Mathematical Physics]] \| issn=0022-2488 \| volume=6 \| pages=1812–1813}}

			==External links==
			*{{citation\|last=Tao\|first=T.\|url=http://terrytao.wordpress.com/2010/07/15/the-golden-thompson-inequality/\|year=2010\|title=The Golden–Thompson inequality}}

			{{DEFAULTSORT:Golden-Thompson inequality}}
			[[Category:Linear algebra]]
			[[Category:Matrix theory]]
			[[Category:Inequalities]]

en>Qetuth: more specific stub type + intro link

2012-01-01T14:13:43Z

more specific stub type + intro link

New page

Nice to satisfy you, my name is Refugia. For many years he's been working as a meter reader and it's something he really enjoy. Minnesota has usually been his home but his spouse wants them to transfer. What I adore doing is to collect badges but I've been taking on new things recently.<br><br>Look at my blog post :: [http://www.buzzbit.net/blog/288042 buzzbit.net]

Householder operator - Revision history

en>Mark viking: Noted interpretation and added a ref

en>Qetuth: more specific stub type + intro link