Least squares solutions of matrix equation AXB=C under semi-tensor product

Abstract

This paper mainly studies the least-squares solutions of matrix equation $ AXB = C $ under a semi-tensor product. According to the definition of the semi-tensor product, the equation is transformed into an ordinary matrix equation. Then, the least-squares solutions of matrix-vector and matrix equations respectively investigated by applying the derivation of matrix operations. Finally, the specific form of the least-squares solutions is given.

Keywords

• matrix equations
• semi-tensor product
• least squares solution