n次幂等正交矩阵集中的等价关系

Equivalence relations on the set of n-potent orthogonal matrices

设R是含幺结合环,n≥2为自然数,Mk(R)为R上的k阶矩阵环,Pnk(R)表示Mk(R)中的n次幂等矩阵集.由n次幂等矩阵正交与代数等价的定义,得到了n次幂等正交矩阵集中2种不同形式的等价关系.

Let R be an associative ring, n≥2 be a natural number, Mk （R） be k th-order matrix ring over R and Pk^n （R） denote the set of n-potents in Mk （R）. Two different equivalence relations on the set of npotent orthogonal matrices are obtained by the definitions of orthogonality and algebraic equivalence about n-potent matrices.