Hadamard powers of rank two, doubly nonnegative matrices
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.03909
- arXiv:
- arXiv:2004.03909
- Bibcode:
- 2020arXiv200403909J
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- Mathematics - Rings and Algebras
- E-Print:
- 12 pages