Least squares solution of F=PG with respect to positive semidefinite symmetric P is considered, a new necessary and sufficient condition for solvablity is given, and the expression of solution is derived in the some special cases. Based on the ex-pression, the least spuares solution of an inverse eigenvalue problem for positive semidefinite symmetric matrices is also given.

Based on the projection theorem m Hfibert space, by making use of the generahzed singular value decompomtion and the canomcal correlation decomposition, an analytical expression of the least-squares solutmn for the matrix equatmn (AXB, GXH)=(C, D) with the minimum-norm is derived An algorithm for finding the minimum-norm solutmn is described and some numerical results have been given

By applying the canonical correlation decomposition (CCD) of matrix pairs, we obtain a general expression of the least-squares solutions of the matrix equa-tion ATXA = D under the restriction that the solution matrix X∈ Rnxn is bisymmetric, where A ∈ Rnxm and D ∈ Rmxm are given matrices.

In this paper, a class of inverse problems of matrix equation AX=B is studied on the linear manifold S={A ∈ SR×n‖AZ-Y‖=min}, the necessary and sufficient conditions for the olvability of the inverse problem and the expression of the general solution are given; at the same time, the best approximation problem is considered, the expression of the best approximate solution and the numerical method are also given. This paper extends the results in [1, 2].

In this paper, four inverse eigenproblems with given three elgenvalues and cor-responding eigenvectors are considered, some necessary and sufficient conditions under which there exists a unique solution for these problems are given. Further-more some numerical algorithms and some numerical experiments are given.