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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.19602 |
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| _version_ | 1866911612082847744 |
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| author | Horn, Roger A. Luo, Shengxuan Xu, Hongwei Yang, Zai |
| author_facet | Horn, Roger A. Luo, Shengxuan Xu, Hongwei Yang, Zai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19602 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Positivity of a Hadamard Product Horn, Roger A. Luo, Shengxuan Xu, Hongwei Yang, Zai Signal Processing 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. |
| title | Positivity of a Hadamard Product |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2604.19602 |