Do the Pseudospectra of a Matrix Determine its Behavior?

Greenbaum, Anne; Trefethen, Lloyd N.

Do the Pseudospectra of a Matrix Determine its Behavior?

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https://hdl.handle.net/1813/6145

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Computer Science Technical Reports

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Author(s)

Greenbaum, Anne

Trefethen, Lloyd N.

Abstract

Let $A$ and $B$ be square matrices. It is shown that the condition $(R)||(z I − A) −1 ||=||(z I − B) −1 ||$ for all $∈\complex$ is equivalent to the condition $(P)|| p (A)||=|| p (B)||$ for all polynomials $p$ if $||⋅||$ is the Frobenius norm, but not if $||⋅||$ is the 2-norm.

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1993-08

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Cornell University

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computer science; technical report

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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR93-1371

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technical report

Do the Pseudospectra of a Matrix Determine its Behavior?

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