Spectrally stable matrices

Terry Lenker; Sivaram Narayan

doi:10.1016/S0024-3795(02)00487-1

Spectrally stable matrices

Terry Lenker, Sivaram Narayan

Mathematics

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

Abstract

Given an n×n complex matrix A define the matrix polytope determined by A as P(A)={AD | D=diag(d"1,...,d(n)),-1d(i)1,i=1,...,n}. We investigate the class of matrices A such that every eigenvalue of every member of P(A) is contained in the convex hull of the eigenvalues of the extreme points of P(A).

Original language	English
Pages (from-to)	177-189
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	362
DOIs	https://doi.org/10.1016/S0024-3795(02)00487-1
State	Published - Mar 15 2003

Keywords

Schur D-stable
Schur stable
Vertex stable

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10.1016/S0024-3795(02)00487-1

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abstract = "Given an n×n complex matrix A define the matrix polytope determined by A as P(A)={AD | D=diag(d{"}1,...,d(n)),-1d(i)1,i=1,...,n}. We investigate the class of matrices A such that every eigenvalue of every member of P(A) is contained in the convex hull of the eigenvalues of the extreme points of P(A).",

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AU - Lenker, Terry

AU - Narayan, Sivaram

PY - 2003/3/15

Y1 - 2003/3/15

N2 - Given an n×n complex matrix A define the matrix polytope determined by A as P(A)={AD | D=diag(d"1,...,d(n)),-1d(i)1,i=1,...,n}. We investigate the class of matrices A such that every eigenvalue of every member of P(A) is contained in the convex hull of the eigenvalues of the extreme points of P(A).

AB - Given an n×n complex matrix A define the matrix polytope determined by A as P(A)={AD | D=diag(d"1,...,d(n)),-1d(i)1,i=1,...,n}. We investigate the class of matrices A such that every eigenvalue of every member of P(A) is contained in the convex hull of the eigenvalues of the extreme points of P(A).

KW - Schur D-stable

KW - Schur stable

KW - Vertex stable

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U2 - 10.1016/S0024-3795(02)00487-1

DO - 10.1016/S0024-3795(02)00487-1

M3 - Article

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SN - 0024-3795

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SP - 177

EP - 189

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Spectrally stable matrices

Abstract

Keywords

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