不可約非負矩陣相似至正矩陣的問題探討

Abstract

我們所要探討的是不可約非負矩陣相似至正矩陣的問題，我們 將探討二個主要問題。一是對於n 階不可約非負矩陣且有n+2 個零元 素和對角線元素皆相異的條件之下，會相似至正矩陣。二是對於n 階 不可約非負矩陣且有n+2 個非零元素的條件之下，會相似至正矩陣。

We study the questions in which the irreducible nonnegative matrices are similar to positive matrices.We will solve the problems for n×n irreducible nonnegative matrices with exactly n+2 zeros, and all the entries of diagonal are distinct, and for n×n irreducible nonnegative matrices with exactly n+2 nonzero elements are similar to positive matrices.