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).
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© 1997 Springer Science+Business Media New York
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Bhatia, R. (1997). Spectral Variation of Nonnormal Matrices. In: Matrix Analysis. Graduate Texts in Mathematics, vol 169. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0653-8_8
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DOI: https://doi.org/10.1007/978-1-4612-0653-8_8
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