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Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations. (English) Zbl 1255.15022

Summary: Within the framework of the theory of the column and row determinants, we obtain explicit representation formulas (analogs of Cramer’s rule) for the minimum norm least squares solutions of quaternion matrix equations \(\mathbf{AX=B,XA=B}\) and \(\mathbf{AXB=D}\).

MSC:

15A24 Matrix equations and identities
15A15 Determinants, permanents, traces, other special matrix functions
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
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