A Generalization of the Complex Autonne-Takagi Factorization To Quaternion Matrices
Linear and Multilinear Algebra
Autonne-Takagi factorization, Complex symmetric matrix, Quaternion matrix, Singular value decomposition, Canonical forms
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.
Horn, Roger A. and Zhang, Fuzhen, "A Generalization of the Complex Autonne-Takagi Factorization To Quaternion Matrices" (2012). Mathematics Faculty Articles. 20.