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arXiv · 1307.5058

A note on solutions of the matrix equation AXB=C

Ivana V. Jovovic·Branko J. Malesevic
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Abstract

This paper deals with necessary and sufficient condition for consistency of the matrix equation $AXB = C$. We will be concerned with the minimal number of free parameters in Penrose's formula $X = A^(1)CB^(1) + Y - A^(1)AYBB^(1)$ for obtaining the general solution of the matrix equation and we will establish the relation between the minimal number of free parameters and the ranks of the matrices A and B. The solution is described in the terms of Rohde's general form of the {1}-inverse of the matrices A and B. We will also use Kronecker product to transform the matrix equation $AXB = C$ into the linear system $(B^T \otimes A)vecX = vec C$.

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Ivana V. Jovovic, Branko J. Malesevic. 2013-07-18. A note on solutions of the matrix equation AXB=C. https://arxiv.org/abs/1307.5058

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