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The singular value decomposition of quaternion matrix with applications. (Chinese. English summary) Zbl 1055.15012

Summary: A constructive proof of the singular value decomposition of a quaternion matrix is given by using the complex representation. A companion vector of the quaternion matrix and a computational method are described. As an application of the singular value decomposition, the CS decomposition is proved and the canonical angles on subspaces of \(Q^n\) are studied.

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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