不可约矩阵与几乎可约矩阵的一些组合性质

摘要 非负矩阵是指元素为非负实数的矩阵，同计算数学，经济数学，概率论，物理，化学等有着密切关系。本论文主要研究非负矩阵的那些仅依赖于矩阵的0元素的位置，而与元素本身数值无关的性质。本论文从非负矩阵的基础理论出发,结合图论的有关性质，利用图论与矩阵的关系，来研究不可约矩阵与几乎可约矩阵的1些性质。 本论文分为3部分，第1章是引言部分，第2章阐述了不可约矩阵，不可约矩阵的谱半径，完全不可分矩阵，几乎可约矩阵，几乎可分矩阵的概念，第3章阐述了不可约矩阵，不可约矩阵的谱半径，完全不可分矩阵，几乎可约矩阵，几乎可分矩阵的重要定理，性质以及其证明。 关键字不可约矩阵；完全不可分矩阵；几乎可约矩阵；几乎可分矩阵；极小强连通图 Abstract Nonnegative Matrices is the

matrices whose elements are nonnegative real numbers, and it has

close relationship with computer science, economic mathematics, the

theorem of probability, physical. This paper mainly research the

matrices’ quality with only depends on zero in matrices, but not its

own values. This paper main research Combinational quality of

Irreducible Matrices and Nearly Reducible Matrices by basic theory

of Nonnegative Matrices , quality of graph theory ,and the

relationship between graph theory and matrices. This paper

includes three parts, the first part is introduction, the second one

expounds the concept of irreducible matrices, spectral radius of

irreducible, fully indecomposable matrices, nearly reducible matrices,

and nearly decomposable matrices. The last one expounds important

theories, qualities and proof of irreducible matrices, spectral

radius of irreducible, fully indecomposable matrices, nearly

reducible matrices, and nearly decomposable matrices.

KeywordIrreducible matrices; Fully indecomposable matrices; Nearly

Reducible matrices; Nearly decomposable matrices; Minimally strong

diagraph.