Analysis of spectral variation and some inequalities

Bhatia, Rajendra (1982) Analysis of spectral variation and some inequalities Transactions of the American Mathematical Society, 272 (1). pp. 323-331. ISSN 0002-9947

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A geometric method, based on a decomposition of the space of complex matrices, is employed to study the variation of the spectrum of a matrix. When adapted to special cases, this leads to some classical inequalities as well as some new ones. As an example of the latter, we show that if U, V are unitary matrices and K is a skew-Hermitian matrix such that UV-1 = exp K, then for every unitary-invariant norm the distance between the eigenvalues of V and those of Vis bounded by ||K||.This generalises two earlier results which used particular unitary-invariant norms.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
ID Code:97445
Deposited On:11 Feb 2013 05:54
Last Modified:19 May 2016 09:36

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