【摘要】 Hadamard利用矩阵对角占优性质提出了著名的矩阵非奇异性判定准则:满足条件|a_ii|>sum from j=1 j≠i to n=1 |a_ij|的矩阵 A=(a_jin×n是非奇异的。Brualdi 在文献[1]中就弱不可约的情况改进了 Hadamard 准则。把按行占优改进为按环路占优,给出了新的判定准则。本文又改进了 Brualdi 的定理,证明了弱非零元素链对角占优矩阵是非奇异的。作为应用给出了 M—矩阵及分块矩阵非奇异性的判定定理。更多还原

【Abstract】 Hadamard has given criterion of nonsingularty of matrices:A matrix A=（a_）n×n is nonsingular matrix,if A sati- sfy condition|a_|>|a_| Brualdi improves Hadamard criterion in paper[1],a new criterion is given. This paper improve Brualdis theorem,We obtain rule as fouovl A matrix is nonsingular matrix if it satisfy weakly diagonally dominant,of chain of nonzero elements.更多还原