关于k-广义Hermite矩阵的研究

Research of k-generalized Hermite matrix

给出了k-广义Hermite矩阵的概念,探讨了它的性质及其与Hermite矩阵、酉矩阵、Hamilton矩阵的广义逆矩阵之间的联系,取得了许多新的结果,推广了酉矩阵、Hermite矩阵及R.D.Hill的广义次对称矩阵间的相应结果,特别是将正交阵的广义Cayley分解推广到了k-广义酉矩阵和k-广义Hermite矩阵上,从而将各类Hermite矩阵及广义逆矩阵统一起来.

The author stated concepts of k-generalized Hermite matrix,its properties and relations with H ermite matrix, unitary matrix, Hamilton matrix and generalized inverse matrix were discussed, with many new results obtained. The corresponding results among unitary matrix, Hermite matrix and generalized symmetric matrix, especially the Cayley decomposition of orthogonal matrix to k- generalized unitary matrix and k-generalized Hermite matrix were extended,and unifying various kinds of the Hermite matrix and generalized inverse matrix.