关于稳定矩阵分解定理的一个简单证明

A Simple Proof for the Decomposition Theorem of Stable Matrices

一个矩阵称为稳定的,如果这个矩阵的特征值全包含在单位开圆盘内.利用Parker关于复方阵的分解定理给出了稳定矩阵分解定理的一个简单证明,并对奇异值全部严格小于1的矩阵给出了类似的结论.

A matrix is said to be stable if all its eigenvalues are contained in the open unit circle.In this paper,by using Parker＇ s theorem on the decomposition theorem for a complex square matrix,we give a simple proof for the decomposition theorem of stable matrices.Moreover,we give similar results for the matrices all of whose singular values are strictly less than 1.