Abstract
This paper deals with necessary and sufficient condition for consistency of the ma- trix 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 param- eters 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 ⊗A)X = C.
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