关于某些特殊分块矩阵的群逆
DOI: 10.3969/j.issn.1006-7043.2009.09.020
Keywords: 群逆 Drazin逆 幂等矩阵 分块矩阵 group inverse Drazin inverse idempotent matrix block matrix
Abstract:
分块矩阵的广义逆不仅在数学理论上有广泛研究而且在自动控制、系统理论、概率统计、数学规划等领域有着广泛的实际研究背景.该文对形如[A B/C 0]分块矩阵的群逆的表达式问题进行了研究.设P是复数域上的幂等阵.令矩阵A,B,C取自集合{P,PP~*,PP~*P },则可以得到27个形如[A B/C 0]的分块矩阵.给出了这27个分块矩阵群逆的存在性与表示形式.
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