Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations

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Abstract

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 AX=B,XA=B and AXB=D.

AMS classification

15A15
16W10

Keywords

Matrix equation
Least squares solution
Moore–Penrose generalized inverse
Quaternion matrix
Cramer rule
Column determinant
Row determinant

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