Tian and Styan have shown many rank equalities for the sum of two and three idempotent matrices and pointed out that rank equalities for the sum P 1 + ⋯+P k with P 1,…, P k be idempotent (k > 3) are still open. In this paper, by using block Gaussian elimination, we obtained rank equalities for the sum of finitely many idempotent matrices and then solved the open problem mentioned above. Extensions to scalar-potent matrices and some related matrices are also included.
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机译：Tian和Styan对两个和三个幂等矩阵的和显示出许多秩相等，并指出对于和P 1 +⋯+ P k和P 1，…，P k是幂等的（k> 3）仍然存在秩相等。打开。在本文中，通过使用块高斯消除，我们获得了有限个幂等矩阵总和的秩相等，然后解决了上述开放问题。还包括对标量有效矩阵和一些相关矩阵的扩展。
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