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

Authors

Roger A. Horn, University of Utah
Fuzhen Zhang, Nova Southeastern UniversityFollow

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

NSUWorks Citation

Horn, Roger A. and Zhang, Fuzhen, "A Generalization of the Complex Autonne-Takagi Factorization To Quaternion Matrices" (2012). Mathematics Faculty Articles. 20.
https://nsuworks.nova.edu/math_facarticles/20

DOI

10.1080/03081087.2011.618838