In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then gi...

— We present an algorithm for computing the irreducible unitary representations of a real reductive group G. The Langlands classification, as formulated by Knapp and Zuckerman, exhibits any representation with an invariant Hermitian form as a deformation of a unitary representation from the Plancherel formula. The behavior of these deformations was in part determined in the Kazhdan-Lusztig anal...

We consider the normwise condition number and backward error of eigenvalues of matrix polynomials having ⋆-palindromic/antipalindromic and ⋆-even/odd structure with respect to structure preserving perturbations. Here ⋆ denotes either the transpose T or the conjugate transpose ∗. We show that when the polynomials are complex and ⋆ denotes complex conjugate, then to each of the structures there c...

We present a circulant and skew-circulant splitting (CSCS) iterative method for solving large sparse continuous Sylvester equations AX+XB=C, where the coefficient matrices A B are Toeplitz matrices. theoretical study shows that if factors of positive semi-definite (not necessarily Hermitian), at least one factor is definite, then CSCS converges to unique solution equation. In addition, our anal...

In this paper, we focus on the following coupled linear matrix equations Mi(X,Y ) = Mi1(X) +Mi2(Y ) = Li, with