Hadamard powers of some positive matrices

Authors

Tanvi Jain, Indian Statistical Institute (Delhi Centre)

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

Comments

Open Access, Bronze, Green

Recommended Citation

Jain, Tanvi, "Hadamard powers of some positive matrices" (2017). Journal Articles. 2449.
https://digitalcommons.isical.ac.in/journal-articles/2449