复矩阵的复对称性
Complex Symmetries of Complex Matrices
DOI: 10.12677/AAM.2022.115310, PDF,    科研立项经费支持
作者: 贾思怡, 刘思彤*, 李 然：辽宁师范大学数学学院，辽宁 大连
关键词: 复矩阵；共轭算子；复对称算子；Complex Matrix； Conjugate Operator； Complex Symmetric Operator
摘要: 本文主要研究复矩阵的复对称问题。通过将2 × 2复矩阵转化为上三角矩阵，研究上三角矩阵的共轭算子，再根据原复矩阵酉等价于上三角矩阵以及它的每一个位置去构造共轭算子，使得这个复矩阵关于此共轭算子是复对称的，进而证明出任意2 × 2复矩阵都是复对称的。
Abstract: In this paper, complex symmetry of complex matrices is studied. By transforming 2 × 2 complex matrix into upper triangular matrix, the conjugate operator of the upper triangular matrix is stud-ied, and then the conjugate operator is constructed according to the unitary equivalent of the origi-nal complex matrix to the upper triangular matrix and every position of it, so that the complex ma-trix is complex symmetric with respect to the conjugate operator, and then it is proved that any 2 × 2 complex matrix is complex symmetric.
文章引用：贾思怡, 刘思彤, 李然. 复矩阵的复对称性[J]. 应用数学进展, 2022, 11(5): 2919-2926. https://doi.org/10.12677/AAM.2022.115310

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