On Solutions of the Matrix Equation A ∘ l X = B with respect to M M -2 Semitensor Product

Abstract

$MM$ -2 semitensor product is a new and very useful mathematical tool, which breaks the limitation of traditional matrix multiplication on the dimension of matrices and has a wide application prospect. This article aims to investigate the solutions of the matrix equation $A{°}_{l}X=B$ with respect to $MM$ -2 semitensor product. The case where the solutions of the equation are vectors is discussed first. Compatible conditions of matrices and the necessary and sufficient condition for the solvability is studied successively. Furthermore, concrete methods of solving the equation are provided. Then, the case where the solutions of the equation are matrices is studied in a similar way. Finally, several examples are given to illustrate the efficiency of the results.