Properties on centroskew self-conjugate matrix
DUAN Shu-juan
QIN Jian-guo
Abstract：The definition of centroskew self-conjugate matrix and some matrix theories were introduced.It was proved that the transposed matrix AT,and inversion A-1 (|A | ≠ 0) of a centroskew self-conjugate matrix A were still centroskew self-conjugate matrix.The direct product of any two centroskew self-conjugate matrix was centroskew self-conjugate matrix.The A * of an even order centroskew self-conjugate matrix and Am of 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 =(a1,a2,…,an)T ∈ Cn was a characteristic vector of the characteristic value λ0 belonging to a centroskew self-conjugate matrix A ∈ C,VX0 =(an,an-1,…,a1)Twas also a characteristic vector of the characteristic value λ0 belonging to-A.
Keywords：centroskew self-conjugate matrixflip matrixadjoint matrixinverse matrix
Publication Date：2017-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：4( 105-108 )