Positive definiteness of Hadamard exponentials and Hadamard inverses

IF 0.8 3区数学 Q2 MATHEMATICS

Positivity Pub Date : 2024-07-13 DOI:10.1007/s11117-024-01070-3

Takashi Sano

引用次数: 0

Abstract

Let A be a positive semidefinite matrix. It is known that the Hadamard exponential of A is positive semidefinite; it is positive definite if and only if no two columns of A are identical. We give an alternative proof of the latter part with an application to Hadamard inverses.

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哈达玛指数和哈达玛倒数的正定性

设 A 是一个正半inite 矩阵。已知 A 的哈达玛指数是正半有限矩阵；当且仅当 A 中没有两列相同时，它才是正定矩阵。我们给出了后一部分的另一种证明，并将其应用于哈达玛倒数。

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

Positivity 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.