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Least-squares problem for the quaternion matrix equation \(AXB+CYD=E\) over different constrained matrices. (English) Zbl 1278.65049

The authors discuss the least-squares solution with the least norm for the quaternion matrix equation \(AXB +CYD = E\). They make use of the complex representations of quaternion matrices, the Moore-Penrose generalized inverse, the Kronecker product of matrices, and other results and turn it to the least-squares unconstrained problems of a real matrix equation. They clearly state some lemmas and then derive the explicit expression for the solution.

MSC:

65F30 Other matrix algorithms (MSC2010)
65F20 Numerical solutions to overdetermined systems, pseudoinverses
15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A09 Theory of matrix inversion and generalized inverses
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