广义H-矩阵的若干性质

在已有的广义Z-矩阵及广义M-矩阵理论的基础上,通过定义竖块矩阵的比较矩阵,继续给出了广义H-矩阵的定义。从该矩阵与广义Z-矩阵及广义M-矩阵的关系、对角占优、特征值等不同角度分析了广义H-矩阵的若干性质,给出了判别广义H-矩阵的几个充分必要条件。研究广义H-矩阵,对于M-矩阵、H-矩阵及稳定性的研究有着促进作用,为更好的求解广义线性互补问题奠定理论基础,同时,应用于其他相关领域,如均衡论、投入产出等。

Some Properties of Generalized H-Matrix

On the base of generalized Z-matrix and M-matrix's theory, the idea of H-matrix was defined continually by giving the concepts of comparable matrix for vertical block matrix. Some properties of generalized H-matrix were analyzed from different aspects, such as diagonally dominant and the relationship between H-matrix and generalized Z-matrix as well as M-matrix, diagonally dominant and characteristic value, etc. and some necessary and sufficient conditions were given. Researching generalized H-matrix, does good to the research of M-matrix, H-matrix and steady property, which offers better theory for solving generalized linear complementary problem, meanwhile, can also be applied in some irrelative fields, such as balance theory, input-output, etc.