一个不可约矩阵为非奇异H矩阵的判定条件

A critical condition for the matrix as nonsingular H-matrices

目的解决判断一个不可约矩阵为H矩阵的条件。方法采用逻辑推理的方法进行了证明。结果得到了当矩阵为不可约时,判断其为H矩阵的条件。结论此结果对于控制系统的稳定性、特征值分布、线性方程组迭代解等方面都具有重要的理论意义。

Aim It is aimed at finding out the solution to judging an irreducible matrix as an Hmatrices. Methods It is proofed by logical inference method. Results It concludes that when matrix is irreducible matrix, it can be judged as the condition of H-matrices. Conclusion The result has important theory significance for control system stability, characteristic value distribution, and system of linear equations iterative solution.