次对称矩阵的推广和它的某些应用

文［６］于１９６２年首先引入了次对称矩阵的概念，文［１］于１９８９年又引入了方阵的次转置的定义，而文［２］将次转置的定义及其结论推广到一般的矩阵上，并且引入了次特征值，次特征向量及次正定的次对称矩阵的概念，讨论了次对称矩阵的对角化方法及次对称矩阵，次正定的次对称矩阵的一些性质。次对称矩阵在求解线性方程组的近似解及摄动问题上均有应用，而循环矩阵是一类典型的次对称矩阵。本文在文［２］的基础上，将次对称矩阵扩充到复数域上，引入了次Ｈｅｒｍｉｔｅ矩阵，讨论了它的对角化问题和它的某些性质，以及一些应用。

The Extension of Sub-symmetrical Matrix and Its Application

Sub-symmetrical matrix is extended into complex field in this paper.Theideas of sub-Hermitian matrix and sub-positive-defined sub-Hermitian matrix are intro-duced.Diagonalization process as well as their characteristics is discussed and a result simi-lar to Hemitian matrix is obtained. As for its application,operator norm and F-norm of sub-Hermitian matrix are givenin terms of its sub-characteristic value. And then,several important matrix determinantinequalities of sub-positive-defined sub-Hermitian matrix are proved.Finally,perturbation for linear equation system with its coefficient matrix as sub-symmetrical ma-trix is discussed.It is shown that perturbation approximation can be determined by thesub-characteristic value of sub symmetrical matrix.