分块矩阵的一个正定条件及其在线性常微分方程中的应用

A Positive Definite Condition for a Block-Matrix and Its Application to Linear Ordinary Differential Equations

设Ｍ＝是一个实对称的分块矩阵，其中Ａ、Ｂ是正定的，那么Ｍ是正定的当且仅当‖ＡＣＢ‖＜１。

Let be a real symmetric block-matrix with A and B positive definte. Then M is positive definte if and only if. An application for this result to the stability of constant coefficient linear system is presented.