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Least squares Hermitian solution of the matrix equation \((AXB,CXD)=(E,F)\) with the least norm over the skew field of quaternions. (English) Zbl 1145.15303

Summary: By using the complex representations of quaternion matrices, Moore-Penrose generalized inverse and the Kronecker product of matrices, we derive the expression of the least squares Hermitian solution of the matrix equation \((AXB,CXD)=(E,F)\) with the least norm over the skew field of quaternions, and provide a numerical algorithm to calculate the forementioned solution.

MSC:

15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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