The Inverse Problems Of Some Special Matrices Under Constrained Conditions

Rencently, a lot of progress about the inverse problems on the matrices has beenmade. And some special matrices have been used widely in all aspects of theengineering. For example, the anti-centro-symetric matrices have practical applicationsin the information theory, the linear system thory and the linear estimation systemtheory, and the Hamiltion and anti-Hamition matrices in the linear quadratic optimalcontrol and solving algebraic equations. By using the straightening operator, theMoore-Penrose generalized inverse and the singular value decomposition of matrices,this paper discussed the inverse problems on some special matrices and provided thenumerical algorithms and numerical experiments.1the expression of the least squares soluion of the marix equationAXB CYD Ewith the least norm and the least squares soluion of the marixequationAXB C, the left and right inverse eigenvalue problem with a submatrixconstranit and the generalized inverse eigenvalue for anti-centro-symetric matrices.2the expression of the left and right inverse eigenvalue problem with a submatrixconstranit and the general inverse eigenvalue for anti-Hermitian generalized Hamiltonmatrices.3the expression of the left and right inverse eigenvalue problem with a submatrixconstranit and the general inverse eigenvalue for anti-Hermitian generalizedanti-Hamilton matrices.