Article
A Generalization of the Complex Autonne-Takagi Factorization To Quaternion Matrices
Linear and Multilinear Algebra
Document Type
Article
Publication Date
1-1-2012
Keywords
- Autonne-Takagi factorization,
- Complex symmetric matrix,
- Quaternion matrix,
- Singular value decomposition,
- Canonical forms
Disciplines
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.
DOI
10.1080/03081087.2011.618838
Citation Information
Roger A. Horn and Fuzhen Zhang. "A Generalization of the Complex Autonne-Takagi Factorization To Quaternion Matrices" Linear and Multilinear Algebra Vol. 60 Iss. 11-12 (2012) p. 1239 - 1244 ISSN: 0308-1087 Available at: http://works.bepress.com/fuzhen-zhang/11/
Special Issue in memory of Professor Ky Fan
AMS Subject Classifications:: 15A23, 15A33