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Mathematics Faculty Articles
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.
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
Comments
Special Issue in memory of Professor Ky Fan
AMS Subject Classifications:: 15A23, 15A33