Hadamard powers of rank two, doubly nonnegative matrices
Advances in Operator Theory
We study ranks of the rth Hadamard powers of doubly nonnegative matrices and show that the matrix A∘r is positive definite for every n× 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.
Jain, Tanvi, "Hadamard powers of rank two, doubly nonnegative matrices" (2020). Journal Articles. 220.