| 一个矩阵函数及其应用 |
| |
| 引用本文： | 王子文.一个矩阵函数及其应用[J].应用数学与计算数学学报,2014(4):449-453. |
| |
| 作者姓名： | 王子文 |
| |
| 作者单位： | 上海大学理学院,上海200444 |
| |
| 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.
|
| 关 键 词： | Lyapunov矩阵方程 矩阵方程 秩 惯性指数 |
A matrix function with applications |
| |
| WANG Zi-wen.A matrix function with applications[J].Communication on Applied Mathematics and Computation,2014(4):449-453. |
| |
| Authors: | WANG Zi-wen |
| |
| Institution: | WANG Zi-wen(College of Sciences, Shanghai University, Shanghai 200444, China) |
| |
| Abstract: | 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. |
| |
| Keywords: | Lyapunov matrix equation matrix equation rank inertia |
| 本文献已被 维普 等数据库收录！ |
|
