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SPECTRAL CHARACTERIZATIONS FOR HERMITIAN CENTROSYMMETRIC K -MATRICES AND HERMITIAN SKEW-CENTROSYMMETRIC K -MATRICES.
- Source :
-
SIAM Journal on Matrix Analysis & Applications . 2003, Vol. 25 Issue 3, p601-605. 5p. - Publication Year :
- 2003
-
Abstract
- Let A and K be real symmetric matrices with K2 = I. In the article ’A spectral characterization of generalized real symmetric centrosymmetric and generalized real symmetric skew-centrosymmetric matrices’ [D. Tao and M. Yasuda, SIAM J. Matrix Anal. Appl., 23 (2002), pp. 885–895], it was shown that (1) AK = KA if and only if the spectrum of A equals the spectrum of KA up to sign and (2) AK = -KA if and only if the spectrum of A equals the spectrum of KA multiplied by i. This paper extends these spectral characterizations from the case of real symmetric matrices to that of self-adjoint compact linear operators in a complex Hilbert space. Some consequences of these results are mentioned, including an application that describes the correspondence between the spectrum of a real symmetric Toeplitz matrix T and its associated Hankel matrix JT, where J is the so-called exchange matrix. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08954798
- Volume :
- 25
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Matrix Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 12766973
- Full Text :
- https://doi.org/10.1137/S0895479802418835