Short normal paths and spectral variation

Bhatia, Rajendra ; Holbrook, John A. R. (1985) Short normal paths and spectral variation Proceedings of the American Mathematical Society, 94 (3). pp. 377-382. ISSN 0002-9939


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We introduce the notion of a "short normal path" between matrices S and T, that is, a continuous path from S to T consisting of normal matrices and having the same length as the straight line path from S to T. By this means we prove that for certain normal matrices S and T the eigenvalues of S and 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||. In particular, we generalize and provide a new approach to a recent result of Bhatia and Davis treating the case of unitary S and T.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
ID Code:97448
Deposited On:11 Feb 2013 05:56
Last Modified:19 May 2016 09:37

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