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The Re-nonnegative definite solutions to the matrix equation $A X B = C$

Qing Wen Wang; Chang Lan Yang — 1998

Commentationes Mathematicae Universitatis Carolinae

An $n \times n$ complex matrix $A$ is called Re-nonnegative definite (Re-nnd) if the real part of $x^{*} A x$ is nonnegative for every complex $n$ -vector $x$ . In this paper criteria for a partitioned matrix to be Re-nnd are given. A necessary and sufficient condition for the existence of and an expression for the Re-nnd solutions of the matrix equation $A X B = C$ are presented.

Inertias and ranks of some Hermitian matrix functions with applications

Xiang Zhang; Qing-Wen Wang; Xin Liu — 2012

Open Mathematics

Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively. As applications,...

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The Re-nonnegative definite solutions to the matrix equation $A X B = C$

Inertias and ranks of some Hermitian matrix functions with applications

Editors’ Summary of the Special Issue dedicated to the 5th International Conference on Matrix Analysis and Applications

Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation.

The reflexive re-nonnegative definite solution to a quaternion matrix equation.

A new solvable condition for a pair of generalized Sylvester equations.

On solutions to the quaternion matrix equation $A X B + C Y D = E$ .

Advanced Search

Formula preview

Currently displaying 1 – 7 of 7

The Re-nonnegative definite solutions to the matrix equation A X B = C

Inertias and ranks of some Hermitian matrix functions with applications

Editors’ Summary of the Special Issue dedicated to the 5th International Conference on Matrix Analysis and Applications

Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation.

The reflexive re-nonnegative definite solution to a quaternion matrix equation.

A new solvable condition for a pair of generalized Sylvester equations.

On solutions to the quaternion matrix equation A X B + C Y D = E .

The Re-nonnegative definite solutions to the matrix equation $A X B = C$

On solutions to the quaternion matrix equation $A X B + C Y D = E$ .