Linear maps on matrices: the invariance of symmetric polynomials
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چکیده
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15 صفحه اولLinear maps preserving or strongly preserving majorization on matrices
For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...
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It is shown that the correlation functions of the random variables det(λ−X), in which X is a real symmetric N × N random matrix, exhibit universal local statistics in the large N limit. The derivation relies on an exact dual representation of the problem: the k-point functions are expressed in terms of finite integrals over (quaternionic) k × k matrices. However the control of the Dyson limit, ...
متن کاملlinear maps preserving or strongly preserving majorization on matrices
for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...
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In this paper, we show that if an injective map on symmetric matrices n S C satisfies then , , n ABA A B A A B S C , Φ t f A SA S for all n A S C , where f is an injective homomorphism on , is a complex orthogonal matrix and C S f A is the image of A under f applied entrywise.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1977
ISSN: 0024-3795
DOI: 10.1016/0024-3795(77)90064-7