矩阵的正则性的若干条件

ON SOME REGULARITY CONDITIONS FOR MATRICES

设 Cn,n(Rn,n)表示 n×n 复（实）矩阵的空间;Cn（Rn）是 n 维复（实）的向量空间;e1,…,en是 Rn 的典型基。Cn 上范数Φ（只要求弱齐性,即Φ（αx）=αΦ（x）对一切数量α≥0成立）是单调的,如果对任意 Cn 内向量 x=（x1,…,xn）与 y=（y1,…,yn）,|xi|≤|yi|（i=1,…,n）蕴涵Φ（x）≤Φ（y）

A norm F on C^n,the n-dimensional complex coordinate space,is called monotonic if for every x=(x_1,…,x_n) and y=(y_1,…,y_n) in C^n,|x_i|…|y_i|for i1l,…,n implies F(x)…F(y).In the present note,the author usos mono- tonic norms on C^n to investigate some regularity conditions for matrices,and sufficient conditions for the comparison matrix of a matrix to be nonsin- gular M-matrix.These results are used further to obtain connected estimates for spectra of matrices.