几种复对称矩阵及复斜对称矩阵的分解

Factorizations of complex symmetric matrices and complex skew-symmetric matrices

提出一个复矩阵是对称酉矩阵的充要条件,并用逻辑上类似的方法证明一个类似于复对称正规矩阵的复斜对称正规矩阵的分解,最后对复斜对称矩阵得到了类似于复对称矩阵Takagi分解的结论.

It is pointed out that the complex symmetric matrices are the sufficient and necessary condition of the symmetric unitary matrices. The factorization of a complex skew-symmetric normal matrix, which is similar to a complex symmetric normal matrix, was demonstrated using a logically similar method. It is concluded that the Takagi factorizafion of complex symmetric matrices is also applicable to complex skew-symmetric matrices.