与四阶对合矩阵可交换的反对合矩阵

Anti-involutory Matrix Interchangeable With Fourth-order Involutory Matrix

讨论与四阶对合矩阵可交换的反对合矩阵。主要结果如下:对于四阶对合矩阵A,如果A≠±I(I是单位矩阵),那么与A可交换的全体反对合矩阵可以分为四类:±i I、±i A、tr(A)=±2和tr(A)=0。

In this paper,we have discussed the anti-involutory matrices,which can interchange with involutory matrix. The main results are as follows：For a forth-order involutory matrix A,if A≠±I （where I is the identity matrix ）,there are altogether 4 kinds of anti-involutory matrices which can interchange with A including：±iI、±iA、tr（A）=±2 and tr（A）=0.