Schur multipliers on analytic matrix spaces

2014 ◽  
pp. 175-183
Keyword(s):  
Schur Multipliers ◽  
Analytic Matrix ◽  
Matrix Spaces

scholarly journals Matrix Spaces and Schur Multipliers

10.1142/8933 ◽  
2013 ◽  
Author(s):  
Lars-Erik Persson ◽  
Nicolae Popa
Keyword(s):  
Schur Multipliers ◽  
Matrix Spaces

scholarly journals Exact relation between singular value and eigenvalue statistics

2016 ◽  
Vol 05 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Mario Kieburg ◽  
Holger Kösters
Keyword(s):  
Singular Values ◽  
Singular Value ◽  
Specific Class ◽  
Rotation Invariant ◽  
Exact Relation ◽  
Finite Matrix ◽  
Eigenvalue Statistics ◽  
Probability Densities ◽  
Analytical Relations ◽  
Matrix Spaces

We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint densities of the singular values and the eigenvalues for complex random matrices which are bi-unitarily invariant (also known as isotropic or unitary rotation invariant). We prove that each of these joint densities determines the other one. Moreover, we construct an explicit formula relating both joint densities at finite matrix dimension. This relation covers probability densities as well as signed densities. With the help of this relation we derive general analytical relations among the corresponding kernels and biorthogonal functions for a specific class of polynomial ensembles. Furthermore, we show how to generalize the relation between the singular value and eigenvalue statistics to certain situations when the ensemble is deformed by a term which breaks the bi-unitary invariance.

scholarly journals Examples of Chebyshev Sets in Matrix Spaces

1999 ◽  
Vol 99 (1) ◽  
pp. 44-53 ◽  
Author(s):  
A.R Alimov ◽  
H Berens
Keyword(s):  
Chebyshev Sets ◽  
Matrix Spaces

scholarly journals Norms of Schur multipliers

2007 ◽  
Vol 51 (3) ◽  
pp. 743-766 ◽  
Author(s):  
Kenneth R. Davidson ◽  
Allan P. Donsig
Keyword(s):  
Schur Multipliers
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