A generalization of the complex Autonne-Takagi factorization to quaternion matrices

作者：Horn Roger A^*; Zhang Fuzhen

来源：Linear and Multilinear Algebra, 2012, 60(11-12): 1239-1244.

DOI：10.1080/03081087.2011.618838

• Autonne-Takagi factorization
• complex symmetric matrix
• quaternion matrix
• singular value decomposition
• canonical forms

A complex symmetric matrix A can always be factored as A = U Sigma U-T, in which U is complex unitary and Sigma 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.

• 出版日期2012
• 单位东南大学