Matrix Analysis pp 226-252 | Cite as

# Spectral Variation of Nonnormal Matrices

Chapter

## Abstract

In Chapter 6 we saw that if *A* and *B* are both Hermitian or both unitary, then the optimal matching distance *d* (σ(*A*), σ(*B*)) is bounded by ||A — *B* ||. We also saw that for arbitrary normal matrices *A, B* this need not always be true (Example VI.3.13). However, in this case, we do have a slightly weaker inequality *d*(σ(*A*), σ(*B*)) ≤ 3|| *A-B*|| (Theorem VII.4.1). If one of the matrices *A, B* is Hermitian and the other is arbitrary, then we can only have an inequality of the form *d*(σ(*A*), σ(*B*)) ≤ *c(n*)||*A* — B||, where *c(n*) is a constant that grows like log *n* (Problems VI.8.8 and VI.8.9).

## Keywords

Real Eigenvalue Spectral Variation Real Vector Space Hermitian Matrice Monic Polynomial
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1997