Eigenvalues of the sum of matrices from unitary similarity orbits

Chi Kwong Li; Yiu Tung Poon; Nung Sing Sze

doi:10.1137/070699123

Eigenvalues of the sum of matrices from unitary similarity orbits

Chi Kwong Li
, Yiu Tung Poon
, Nung Sing Sze

Research output: Journal article publication › Journal article › Academic research › peer-review

11 Citations (Scopus)

Abstract

Let A and B be n x n complex matrices. Characterization is given for the set ∈{A, B) of eigenvalues of matrices of the form U * AU + V * BV for some unitary matrices U and V, Consequences of the results are discussed and computer algorithms and programs are designed to generate the set ∈(A, B). The results refine those of Wielandt on normal matrices. Extensions of the results to the sum of matrices from three or more unitary similarity orbits are also considered.

Original language	English
Pages (from-to)	560-581
Number of pages	22
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	30
Issue number	2
DOIs	https://doi.org/10.1137/070699123
Publication status	Published - 1 Dec 2008
Externally published	Yes

Keywords

Davis-Wielandt shell
Eigenvalues
Sum of matrices
Unitary similarity orbits

ASJC Scopus subject areas

Analysis

More information

10.1137/070699123

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abstract = "Let A and B be n x n complex matrices. Characterization is given for the set ∈\{A, B) of eigenvalues of matrices of the form U * AU + V * BV for some unitary matrices U and V, Consequences of the results are discussed and computer algorithms and programs are designed to generate the set ∈(A, B). The results refine those of Wielandt on normal matrices. Extensions of the results to the sum of matrices from three or more unitary similarity orbits are also considered.",

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AU - Poon, Yiu Tung

AU - Sze, Nung Sing

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N2 - Let A and B be n x n complex matrices. Characterization is given for the set ∈{A, B) of eigenvalues of matrices of the form U * AU + V * BV for some unitary matrices U and V, Consequences of the results are discussed and computer algorithms and programs are designed to generate the set ∈(A, B). The results refine those of Wielandt on normal matrices. Extensions of the results to the sum of matrices from three or more unitary similarity orbits are also considered.

AB - Let A and B be n x n complex matrices. Characterization is given for the set ∈{A, B) of eigenvalues of matrices of the form U * AU + V * BV for some unitary matrices U and V, Consequences of the results are discussed and computer algorithms and programs are designed to generate the set ∈(A, B). The results refine those of Wielandt on normal matrices. Extensions of the results to the sum of matrices from three or more unitary similarity orbits are also considered.

KW - Davis-Wielandt shell

KW - Eigenvalues

KW - Sum of matrices

KW - Unitary similarity orbits

UR - https://www.scopus.com/pages/publications/67649206988

U2 - 10.1137/070699123

DO - 10.1137/070699123

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ER -

Eigenvalues of the sum of matrices from unitary similarity orbits

Abstract

Keywords

ASJC Scopus subject areas

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