Anti-idempotency of linear combinations of anti-idempotent matrices are investigated. A result that diagonalization matrices are expressed to linear combinations of antiidempotent matrices is given. Also, we obtain a pathway of constructive anti-idempotent matrices of pairwise commutaive and orthogonal.%讨论了反幂等阵线性组合的幂等性,指出可对角化矩阵可表示为反幂等阵的线性组合,并由此得到了由非奇异矩阵构造两两正交且可交换的反幂等阵的一种方法.
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