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arXiv · 2004.03909

Hadamard powers of rank two, doubly nonnegative matrices

Tanvi Jain
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Abstract

We study ranks of the $r\textrm{th}$ Hadamard powers of doubly nonnegative matrices and show that the matrix $A^{\circ r}$ is positive definite for every $n\times n$ doubly nonnegative matrix $A$ and for every $r>n-2$ if and only if no column of $A$ is a scalar multiple of any other column of $A.$ A particular emphasis is given to the study of rank, positivity and monotonicity of Hadamard powers of rank two, positive semidefinite matrices that have all entries positive.

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Tanvi Jain. 2020-04-08. Hadamard powers of rank two, doubly nonnegative matrices. https://arxiv.org/abs/2004.03909

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