en>Well-rested: Accounting

2014-01-18T16:16:45Z

Accounting

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	~~Hi there~~, ~~I am Sophia~~. ~~What me~~ and ~~my family members adore~~ is ~~bungee jumping but I've been using on new things recently~~. ~~Mississippi~~ is the ~~only location I~~'~~ve been residing in but I will have to move in~~ a ~~yr or two~~. ~~Distributing production~~ is ~~exactly~~ where ~~her main income arrives from.~~<br><br>~~My homepage -~~ [~~http:~~/~~/checkmates~~.co.~~za/index~~.~~php?do~~=/~~profile-56347~~/~~info~~/ ~~psychic chat online~~]		:''Immanant redirects here; it should not be confused with the philosophical [[Immanence\|immanent]].''

			In mathematics, the '''immanant of a matrix''' was defined by [[Dudley E. Littlewood]] and [[Archibald Read Richardson]] as a generalisation of the concepts of [[determinant]] and [[permanent]].

			Let <math>\lambda=(\lambda_1,\lambda_2,\ldots)</math> be a [[Partition_%28number_theory%29\|partition]] of <math>n</math> and let <math>\chi_\lambda</math> be the corresponding irreducible [[Group representation\|representation-theoretic]] [[Character_%28group_theory%29\|character]] of the [[symmetric group]] <math>S_n</math>. The ''immanant'' of an <math>n\times n</math> [[Matrix_%28mathematics%29\|matrix]] <math>A=(a_{ij})</math> associated with the character <math>\chi_\lambda</math> is defined as the expression

			:<math>{\rm Imm}_\lambda(A)=\sum_{\sigma\in S_n}\chi_\lambda(\sigma)a_{1\sigma(1)}a_{2\sigma(2)}\cdots a_{n\sigma(n)}.</math>

			The determinant is a special case of the immanant, where <math>\chi_\lambda</math> is the [[alternating character]] <math>\sgn</math>, of ''S''<sub>''n''</sub>, defined by the [[parity of a permutation]].

			The permanent is the case where <math>\chi_\lambda</math> is the [[trivial character]], which is identically equal to 1.

			Littlewood and Richardson also studied its relation to [[Schur function]]s in the [[representation theory of the symmetric group]].

			==References==

			* {{cite journal \| author=D.E. Littlewood \| authorlink=Dudley E. Littlewood \| coauthors=[[Archibald Read Richardson\|A.R. Richardson]] \| title=Group characters and algebras \| journal=[[Philosophical Transactions of the Royal Society A]] \| year=1934 \| volume=233 \| pages=99–124 \| doi=10.1098/rsta.1934.0015 \| issue=721–730 }}

			* {{cite book \| author=D.E. Littlewood \| authorlink=Dudley E. Littlewood \| title=The Theory of Group Characters and Matrix Representations of Groups \| edition=2nd \| year=1950 \| publisher=Oxford Univ. Press (reprinted by AMS, 2006) \| page=81 }}

			==External links==
			*[http://planetmath.org/encyclopedia/Immanent.html Immanent] at ''[[PlanetMath]]''

			[[Category:Algebra]]
			[[Category:Linear algebra]]
			[[Category:Matrix theory]]
			[[Category:Permutations]]

en>Lockley: remove context tag

2012-06-19T14:23:56Z

remove context tag

New page

Hi there, I am Sophia. What me and my family members adore is bungee jumping but I've been using on new things recently. Mississippi is the only location I've been residing in but I will have to move in a yr or two. Distributing production is exactly where her main income arrives from.<br><br>My homepage - [http://checkmates.co.za/index.php?do=/profile-56347/info/ psychic chat online]

Earnings response coefficient - Revision history

en>Well-rested: Accounting

en>Lockley: remove context tag