Least-squares solution with the minimum-norm for the matrix equation ( AXB, GXH) = ( C, D)

Abstract

Based on the projection theorem in Hilbert space, by making use of the generalized singular value decomposition and the canonical correlation decomposition, an analytical expression of the least-squares solution for the matrix equation ( AXB, GXH) = ( C, D) with the minimum-norm is derived. An algorithm for finding the minimum-norm solution is described and some numerical results have been given.