【摘要】 本文重新论述有界灰方阵的非奇异性判别问题,提出“条件非奇异”与“最大非奇异子元值域”的新概念,指出现有结果的局限性,给出了一些实用判据,并对灰逆阵的存在性条件与定义域作了研究.此外,本文又提出有界灰矩阵的“灰秩”的新概念与算法,建立了有界灰矩阵恒满秩、恒不满秩、条件满秩的判据。更多还原

【Abstract】 The judgement problem of the nonsingularity of a bounded square grey matrix is reconsidered. and the new concepts of “conditional nonsingularity” and “maximum nonsingular sub-element-value-region” are proposed. Showing the limitation of existing results, some practical criteria are given. The existence conditions and definition region of a grey inverse matrix are studied. Additionally , the new concept of grey rank of a bounded grey matrix and its algorithm are proposed and the criteria for constant-full-rank, constant-non-full-rank, conditional-full-rank of a bounded grey matrix are given.更多还原