# Positivity of a Hadamard Product

arXiv: https://arxiv.org/abs/2604.19602 · HTML: https://mlsanity.com/paper/2604.19602/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Apr 2026.

## Built on by (most cited first, 1 of 1)

- [CP-factorization for high dimensional tensor time series and double projection iterations](https://mlsanity.com/paper/2606.08560/) (2026)

## Abstract (arXiv)

A notable difference between the ordinary and Hadamard products is that the Hadamard product of two singular positive semidefinite matrices can be nonsingular, and one of the factors can even be indefinite. We present an eigenvalue lower bound for a Hadamard product that depends on the rank, effective condition number, and diagonal entries of one factor, and the smallest eigenvalues of certain principal submatrices of the other factor. We give numerical examples and discuss its applications in array signal processing and matrix time series analysis.