A New Canonical Form for Complex Symmetric Matrices

Scott, N. H. (1993) A New Canonical Form for Complex Symmetric Matrices. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 441 (1913). pp. 625-640. ISSN 1364-5021

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Abstract

It is well known that every real symmetric matrix, and every (complex) hermitian matrix, is diagonalizable, i. e. orthogonally similar to a diagonal matrix. However, a complex symmetric matrix with repeated eigenvalues may fail to be diagonalizable. We present a block diagonal canonical form, in which each block is quasi-diagonal, to which every complex symmetric matrix is orthogonally similar. As far as applications are concerned, complex symmetric matrices, as opposed to hermitian matrices, play an important role in theories of wave propagation in continuous media (e. g. elasticity, thermoelasticity).

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:23
Last Modified: 15 Dec 2022 02:08
URI: https://ueaeprints.uea.ac.uk/id/eprint/20846
DOI: 10.1098/rspa.1993.0083

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