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 .
The Re-nonnegative definite solutions to the matrix equation
An complex matrix is called Re-nonnegative definite (Re-nnd) if the real part of is nonnegative for every complex -vector . 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 are presented.
Inertias and ranks of some Hermitian matrix functions with applications
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,...
Editors’ Summary of the Special Issue dedicated to the 5th International Conference on Matrix Analysis and Applications
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