#### Title

### 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