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Quaternion generalized singular value decomposition and its applications. (English) Zbl 1093.15014

The authors derive a theorem of the generalized singular value decomposition of quaternion matrices(QGSVD), study the solution of general quaternion matrix equation \(\mathcal{AXB-CYD=E}\), and obtain a quaternionic Roth’s theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.

MSC:

15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A18 Eigenvalues, singular values, and eigenvectors
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References:

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