摘要
引入反中心自共轭矩阵的定义和相关矩阵理论,证明了如下命题:1)反中心自共轭矩阵A的转置矩阵A^T,逆矩阵A^(-1)(A≠0)仍为反中心自共轭矩阵;2)任意两个反中心自共轭矩阵的直积为反中心自共轭矩阵;3)反中心自共轭矩阵A的伴随矩阵A~*(当A的阶数为偶数时)和A^m(当m为奇数时)仍为反中心自共轭矩阵;4)反中心自共轭矩阵A与-A有相同的特征值,且当0≠X_0=(a_1,a_2,…,a_n)~T∈C^n是属于反中心自共轭矩阵A∈C^(n×n)的特征值λ_0的任一特征向量时,VX_0=(a_n,a_(n-1),…,a_1)T是属于-A的特征值λ_0的特征向量.
The definition of centroskew self-conjugate matrix and some matrix theories were introduced. It was proved that the transposed matrix A1, and inversion A （ ｜ A ｜ ≠ 0） of a centroskew self-conjugate m atrix A were still centroskew self-conjugate matrix. The direct product of any two centroskew self-conjugate matrix was centroskew self-conjugate matrix. The A ＊ o f an even order centroskew self-conjugate matrix and o f the odd number degree power were still centroskew self-conjugate matrix. When the centroskew self-conjugate matrix of A and -A had the same characteristic values, and 0≠X0 = （ a 1,a 2,…,an） T ∈ C n was a characteristic vector of the characteristic value λ0 belonging to a centroskew self-conjugate matrix A ∈ C m×n VX0 = （an,an-1,…, a1）T was also a characteristic vector of the characteristic value λ0 belonging to - A .
出处
《轻工学报》
CAS
2017年第6期105-108,共4页
Journal of Light Industry
基金
国家自然科学基金项目(11501526)
关键词
反中心自共扼矩阵
翻转矩阵
伴随矩阵
逆矩阵
centroskew self-conjugate matrix
flip matrix
adjoint matrix
inverse matrix
