摘要
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.
出处
《应用数学与计算数学学报》
2014年第4期449-453,共5页
Communication on Applied Mathematics and Computation