【摘要】 利用分块矩阵作为工具,对幂等矩阵的一个结论进行了推广,给出当秩为r的n阶幂等矩阵A分解为m个秩为ri的矩阵Ai之和时,在一定条件下,总存在可逆矩阵T,使T-1AT和T-1AiT(i=1,2,...,m)都是简化的准对角形矩阵。更多还原

【Abstract】 Using block matrix as a tool,popularization of a conclusion for idempotent matrix is made.when a n×n idempotent matrix of rank r is decomposed into sum of m matrix Ai of rank ri,under certain conditions,the existence of a invertible matrix T satisfying T-1AT and T-1AiT(i=1,2,...,m) all being simplified quasi-diagonal matrix is proved.更多还原