Liu, Yonghui; Jiang, Tongsong; Wei, Musheng The singular value decomposition of quaternion matrix with applications. (Chinese. English summary) Zbl 1055.15012 Numer. Math., Nanjing 25, No. 4, 321-328 (2003). 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.) Keywords:quaternion matrix; singular value decomposition; CS decomposition; canonical angle PDFBibTeX XMLCite \textit{Y. Liu} et al., Numer. Math., Nanjing 25, No. 4, 321--328 (2003; Zbl 1055.15012)