Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Analysis of spectral variation and some inequalities


Author: Rajendra Bhatia
Journal: Trans. Amer. Math. Soc. 272 (1982), 323-331
MSC: Primary 15A42; Secondary 15A60, 53A45
DOI: https://doi.org/10.1090/S0002-9947-1982-0656492-X
MathSciNet review: 656492
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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 $ U{V^{ - 1}} = \exp K$, then for every unitary-invariant norm the distance between the eigenvalues of $ U$ and those of $ V$ is bounded by $ \vert\vert K\vert\vert$. This generalises two earlier results which used particular unitary-invariant norms.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 15A42, 15A60, 53A45

Retrieve articles in all journals with MSC: 15A42, 15A60, 53A45


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0656492-X
Keywords: Unitary-invariant norm, eigenvalue, singular value, submanifold, tangent space, $ {C^1}$ functions
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society