Estimates for the eigenvalues of the Jordan product of Hermitian matrices

N Alikakos; P W Bates

doi:10.1016/0024-3795(84)90175-7

Estimates for the eigenvalues of the Jordan product of Hermitian matrices

N Alikakos
, P W Bates

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

Given Hermitian matrices A and B, Professor Taussky-Todd posed the problem of estimating the eigenvalues of their Jordan product AB+BA. Here we establish bounds for all the eigenvalues of the Jordan product when both A and B are positive definite. At the same time we give a more straightforward proof and an improvement of estimates given by D. W. Nicholson for the smallest eigenvalue. © 1984.

Original language	English
Pages (from-to)	41-56
Number of pages	16
Journal	Linear Algebra and Its Applications
Volume	57
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(84)90175-7
Publication status	Published - Feb 1984

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title = "Estimates for the eigenvalues of the Jordan product of Hermitian matrices",

abstract = "Given Hermitian matrices A and B, Professor Taussky-Todd posed the problem of estimating the eigenvalues of their Jordan product AB+BA. Here we establish bounds for all the eigenvalues of the Jordan product when both A and B are positive definite. At the same time we give a more straightforward proof and an improvement of estimates given by D. W. Nicholson for the smallest eigenvalue. {\textcopyright} 1984.",

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AU - Bates, P W

PY - 1984/2

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N2 - Given Hermitian matrices A and B, Professor Taussky-Todd posed the problem of estimating the eigenvalues of their Jordan product AB+BA. Here we establish bounds for all the eigenvalues of the Jordan product when both A and B are positive definite. At the same time we give a more straightforward proof and an improvement of estimates given by D. W. Nicholson for the smallest eigenvalue. © 1984.

AB - Given Hermitian matrices A and B, Professor Taussky-Todd posed the problem of estimating the eigenvalues of their Jordan product AB+BA. Here we establish bounds for all the eigenvalues of the Jordan product when both A and B are positive definite. At the same time we give a more straightforward proof and an improvement of estimates given by D. W. Nicholson for the smallest eigenvalue. © 1984.

UR - https://www.scopus.com/pages/publications/26844452490

U2 - 10.1016/0024-3795(84)90175-7

DO - 10.1016/0024-3795(84)90175-7

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SN - 0024-3795

VL - 57

SP - 41

EP - 56

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

Estimates for the eigenvalues of the Jordan product of Hermitian matrices

Abstract

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