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Article
A Generalization of the Complex Autonne-Takagi Factorization To Quaternion Matrices
Linear and Multilinear Algebra
  • Roger A. Horn, University of Utah
  • Fuzhen Zhang, Nova Southeastern University
Document Type
Article
Publication Date
1-1-2012
Keywords
  • Autonne-Takagi factorization,
  • Complex symmetric matrix,
  • Quaternion matrix,
  • Singular value decomposition,
  • Canonical forms
Disciplines
Peer Reviewed
1
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
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/