体上一类具有幂等子块的分块矩阵的群逆
DOI: 10.3969/j.issn.1006-7043.2009.10.019
Keywords: 体 分块矩阵 幂等矩阵 群逆 skew field block matrix idempotent matrix group inverse
Abstract:
设K是一个体, K_(m×n)表示m×n上所有K矩阵的集合.对矩阵A∈K 若存在矩阵X∈K_(n×n)使AXA=A,XAX=X,AX=XA,则称X为A的群逆.研究分块矩阵广义逆的表达式是矩阵广义逆理论中研究的重要问题.分块矩阵的群逆表达式在奇异微分和差分方程、马尔可夫链、迭代方法和密码学等领域有广泛应用.这里给出了体上分块矩阵[ABB0](A,B∈K_(n×n),B~2=B,((I-B)A)~#存在)的群逆的存在性及表示形式.
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