Short normal paths and spectral variation-Reference-Cited by-同舟云学术

Short normal paths and spectral variation

Published:1985 Issue:3 Volume:94 Page:377-382
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Bhatia Rajendra,Holbrook John A. R.

Abstract

We introduce the notion of a "short normal path" between matrices S S and T T , that is, a continuous path from S S to T T consisting of normal matrices and having the same length as the straight line path from S S to T T . By this means we prove that for certain normal matrices S S and T T the eigenvalues of S S and T T may be paired in such a way that the maximum distance (in the complex plane) between the pairs is no more than the operator norm ‖ S − T ‖ \left \| {S - T} \right \| . In particular, we generalize and provide a new approach to a recent result of Bhatia and Davis treating the case of unitary S S and T T .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1985-094-03/S0002-9939-1985-0787876-5/S0002-9939-1985-0787876-5.pdf

Reference6 articles.

1. Analysis of spectral variation and some inequalities;Bhatia, Rajendra;Trans. Amer. Math. Soc.,1982

2. A bound for the spectral variation of a unitary operator;Bhatia, Rajendra;Linear and Multilinear Algebra,1984

3. T. Kato, Perturbation theory for linear operators, Springer-Verlag, Berlin and New York, 1980.

4. Symmetric gauge functions and unitarily invariant norms;Mirsky, L.;Quart. J. Math. Oxford Ser. (2),1960

5. Distance between normal operators;Sunder, V. S.;Proc. Amer. Math. Soc.,1982

Cited by 12 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On Specht's Theorem in UHF C⁎-algebras;Journal of Functional Analysis;2021-01

2. The Mathematics of Chandler Davis;The Mathematical Intelligencer;2014-01-11

3. Spectral variation, normal matrices, and finsler geometry;The Mathematical Intelligencer;2007-06

4. On the Perturbation Theory for Unitary Eigenvalue Problems;SIAM Journal on Matrix Analysis and Applications;2000-01

5. The Hoffman-Wielandt inequality in infinite dimensions;Proceedings Mathematical Sciences;1994-08