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2011•arXiv (Cornell University)Open access

On The Best Approximate Solutions of The Matrix Equation $AXB=C$

Halim Özdemır, Murat Sarduvan

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Abstract

Suppose that the matrix equation $AXB=C$ with unknown matrix $X$ is given, where $A$, $B$, and $C$\ are known matrices of suitable sizes. The matrix nearness problem is considered over the general and least squares solutions of the matrix equation $AXB=C$ when the equation is consistent and inconsistent, respectively. The implicit form of the best approximate solutions of the problems over the set of symmetric and the set of skew-symmetric matrices are established as well. Moreover, some numerical examples are given for the problems considered.

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Suppose that the matrix equation $AXB=C$ with unknown matrix $X$ is given, where $A$, $B$, and $C$\ are known matrices of suitable sizes. The matrix nearness problem is considered over the general and least squares solutions of the matrix equation $AXB=C$ when the equation is consistent and inconsistent, respectively. The implicit form of the best approximate solutions of the problems over the set of symmetric and the set of skew-symmetric matrices are established as well. Moreover, some numerical examples are given for the problems considered.

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Available abstract

Suppose that the matrix equation $AXB=C$ with unknown matrix $X$ is given, where $A$, $B$, and $C$\ are known matrices of suitable sizes. The matrix nearness problem is considered over the general and least squares solutions of the matrix equation $AXB=C$ when the equation is consistent and inconsistent, respectively. The implicit form of the best approximate solutions of the problems over the set of symmetric and the set of skew-symmetric matrices are established as well. Moreover, some numerical examples are given for the problems considered.

Key concepts: Mathematics, Matrix (chemical analysis), Matrix difference equation, Applied mathematics, Set (abstract data type), Symmetric matrix, Skew-symmetric matrix, Square matrix

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