一个矩阵函数及其应用(英文)

A matrix function with applications

给出了矩阵函数f(X)=A-BX-(BX)*的秩和最小惯性指数定理,其中*表示矩阵的共轭转置.作为应用,给出了Lyapunov矩阵方程以及矩阵不等式BX+(BX)*≥A和BX+(BX)*≤A可解的若干充要条件.

In this paper,we give a rank and inertia minimization theorem on a matrix function f（X） = A- BX-（BX）＊,where ＊ means the transpose and conjugate of a matrix.As applications,we give some necessary and sufficient conditions for the Lyapunov matrix equation and matrix inequalities BX ＋（BX）＊ ≥ A and BX ＋（BX）＊ ≤ A to be solvable.