# Hadamard powers of some positive matrices

## Article Type

Research Article

## Publication Title

Linear Algebra and Its Applications

## Abstract

Positivity properties of the Hadamard powers of the matrix [1+xixj] for distinct positive real numbers x1,…,xn and the matrix [|cos((i−j)π/n)|] are studied. In particular, it is shown that the n×n matrix [(1+xixj)r] is positive semidefinite if and only if r is a nonnegative integer or r>n−2, and for every odd integer n≥3 the n×n matrix [|cos((i−j)π/n)|r] is positive semidefinite if and only if r is a nonnegative even integer or r>n−3.

## First Page

147

## Last Page

158

## DOI

10.1016/j.laa.2016.06.030

## Publication Date

9-1-2017

## Recommended Citation

Jain, Tanvi, "Hadamard powers of some positive matrices" (2017). *Journal Articles*. 2449.

https://digitalcommons.isical.ac.in/journal-articles/2449

## Comments

Open Access, Bronze, Green