A generalization of the complex Autonne–Takagi factorization to quaternion matrices
Roger A. Horn, Fuzhen Zhang · Linear and Multilinear Algebra · 2011
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.