不可約非負矩陣相似至正矩陣的問題探討

Irreducible nonnegative matrices that are similar to positive matrices

王信元(Hsin-Yuan Wang)

指導教授 ： 王國仲

國立交通大學/理學院/應用數學系暨研究所/碩士(2011年)

https://doi.org/10.6842/NCTU.2011.00563

摘要

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。

關鍵字

不可約 ； 非負矩陣 ； 相似 ； 正矩陣

並列摘要

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.

並列關鍵字

irreducible ； nonnegative matrices ； similar ； positive matricers

參考文獻

[1] A. Borobia, J. Moro, On nonnegative matrices similar to positive matrices.

Linear Algebra Appl., 266 (1997), pp. 365{379.

[3] T. J. Laey, Extreme nonnegative matrices, Linear Algebra Appl., 275/276

[4] H. Minc, Nonnegative matrices, Wiley, New York, 1988.

[2] T. J. Laey, Raphael Loewy, Helena Smigoc, Nonnegative matrices that