摘要
非負矩陣是指元素爲非負實數的矩陣，同計算數學，經濟數學，概率論，物理，化學等有着密切關係。本論文主要研究非負矩陣的那些僅依賴於矩陣的0元素的`位置，而與元素本身數值無關的性質。
本論文從非負矩陣的基礎理論出發,結合圖論的有關性質，利用圖論與矩陣的關係，來研究不可約矩陣與幾乎可約矩陣的1些性質。
本論文分爲3部分，第1章是引言部分，第2章闡述了不可約矩陣，不可約矩陣的譜半徑，完全不可分矩陣，幾乎可約矩陣，幾乎可分矩陣的概念，第3章闡述了不可約矩陣，不可約矩陣的譜半徑，完全不可分矩陣，幾乎可約矩陣，幾乎可分矩陣的重要定理，性質以及其證明。
關鍵字
不可約矩陣；完全不可分矩陣；幾乎可約矩陣；幾乎可分矩陣；極小強連通圖
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.
Keyword
Irreducible matrices; Fully indecomposable matrices; Nearly Reducible matrices; Nearly decomposable matrices; Minimally strong diagraph.