Schur decompositions of a matrix and the boundary of its pseudospectrum

Lyonell Boulton; Peter Lancaster

doi:10.1137/070682642

Schur decompositions of a matrix and the boundary of its pseudospectrum

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Abstract

We discuss the notion of irreducible block Schur decomposition of a complex square matrix and show how such a decomposition provides information about singularities in the boundaries of pseudospectra of the matrix. Detailed examples are provided to illustrate the theory. © 2010 Society for Industrial and Applied Mathematics.

Original language	English
Pages (from-to)	2921-2933
Number of pages	13
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	31
Issue number	5
DOIs	https://doi.org/10.1137/070682642
Publication status	Published - 2010

Keywords

Irreducible block Schur decomposition
Path-following algorithms
Pseudospectra of linear transformations
Schur triangular form

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abstract = "We discuss the notion of irreducible block Schur decomposition of a complex square matrix and show how such a decomposition provides information about singularities in the boundaries of pseudospectra of the matrix. Detailed examples are provided to illustrate the theory. {\textcopyright} 2010 Society for Industrial and Applied Mathematics.",

keywords = "Irreducible block Schur decomposition, Path-following algorithms, Pseudospectra of linear transformations, Schur triangular form",

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AB - We discuss the notion of irreducible block Schur decomposition of a complex square matrix and show how such a decomposition provides information about singularities in the boundaries of pseudospectra of the matrix. Detailed examples are provided to illustrate the theory. © 2010 Society for Industrial and Applied Mathematics.

KW - Irreducible block Schur decomposition

KW - Path-following algorithms

KW - Pseudospectra of linear transformations

KW - Schur triangular form

U2 - 10.1137/070682642

DO - 10.1137/070682642

M3 - Article

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JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

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Schur decompositions of a matrix and the boundary of its pseudospectrum

Abstract

Keywords

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