Spectral Variation of Nonnormal Matrices

  • Rajendra Bhatia
Part of the Graduate Texts in Mathematics book series (GTM, volume 169)


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).


Hull Cond IllY 


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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Rajendra Bhatia
    • 1
  1. 1.Indian Statistical InstituteNew DelhiIndia

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