关于次(反)自共轭矩阵的几个性质

Some properties on self-conjugate matrix and inverse self-conjugate matrixabout secondary diagonal

给出次(反)自共轭矩阵的定义,按定义并运用旋转矩阵,给出次(反)自共轭矩阵的一些性质.首先证明次自共轭矩阵A,B的和,实数k与A的乘积,A的2k次幂及A-1仍是次自共轭矩阵;其次给出次反自共轭矩阵的一些与次自共轭矩阵类似的性质和它的一个特殊性质,最后讨论次自共轭矩阵与Hermite矩阵之间的关系并给出任意A可表为一个次自共轭矩阵和一个次反自共轭矩阵之和的结论.

Some properties on self-conjugate matrix and inverse self-conjugate matrix about secondary diagonal are studied.Firstly,letting A and B be self-conjugate matrices about secondary diagonal,A+B,kA(k∈R).A^(2^k),the accompanying matrix of A,A^(-1) are also investigated to be Secondly,some similar properties and a special one of inverse self-conjugate matrices about secondary diagonal are discussed.Finally,the mutual relations between self-conjugate matrix about secondary diagonal and Hermite matrix and a formula of D∈Q^(n×n),D=E+F are obtained (E,F is self-conjugate matrix and inverse matrix about secondary diagonal respectively.