P-matrix powers

IF 1 3区数学 Q1 MATHEMATICS Linear Algebra and its Applications Pub Date : 2024-07-06 DOI:10.1016/j.laa.2024.07.002

引用次数: 0

Abstract

A P-matrix is a matrix all of whose principal minors are positive. We demonstrate that the fractional powers of a P-matrix are also P-matrices. This insight allows us to affirmatively address a longstanding conjecture raised in Hershkowitz and Johnson (1986) [8]: It is shown that if $A^{k}$ is a P-matrix for all positive integers k, then the eigenvalues of A are positive.

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P 矩阵幂

-矩阵是指所有主减数都为正的矩阵。我们证明了-矩阵的分数幂也是-矩阵。这一洞察力使我们能够肯定地解决赫什科维茨和约翰逊（1986）提出的一个长期猜想：如果对于所有正整数是一个-矩阵，那么它的特征值是正的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.

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