Mathematics Faculty Articles

Title

A Generalization of the Complex Autonne-Takagi Factorization To Quaternion Matrices

Document Type

Article

Publication Date

2012

Publication Title

Linear and Multilinear Algebra

Keywords

Autonne-Takagi factorization, Complex symmetric matrix, Quaternion matrix, Singular value decomposition, Canonical forms

ISSN

0308-1087

Volume

60

Issue/No.

11-12

First Page

1239

Last Page

1244

Abstract

A complex symmetric matrix A can always be factored as A = UΣU T , in which U is complex unitary and Σ is a real diagonal matrix whose diagonal entries are the singular values of A. This factorization may be thought of as a special singular value decomposition for complex symmetric matrices. We present an analogous special singular value decomposition for a class of quaternion matrices that includes complex matrices that are symmetric or Hermitian.

Comments

Special Issue in memory of Professor Ky Fan

AMS Subject Classifications:: 15A23, 15A33

DOI

10.1080/03081087.2011.618838

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Peer Reviewed

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