The Several Inverse Problems Of Anti-Symmetric Ortho-Symmetric Matrices

Let P∈R^n×n be a orthogonal symmetric matrix, A ∈R^n×n is called a anti-symmetric ortho-symmetric matrix, if A^T = —A and (PA)^T = PA. The set ofall nxn anti-symmetric ortho-symmetric matrices is denoted by ASOSR_P^n×n .This paper discusses the several inverse problems of anti-symmetric ortho-symmetric matrices. i.e. the sufficient and necessary conditions for thesolvability solutions to AX = B, AX = XΛ, X^T AX = B , and theLeast-square solutions of f(A)=||AX - Z||² +||Y^T A-W^T||²= minare derived .Theexpressions of the general solutions for these problems are given . The optimal approximate solution to a given matrix is provided. Meanwhile, numerical algorithms for the solutions are also given.