Negativity-preserving transforms of tuples of symmetric matrices
arxiv(2023)
摘要
Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We achieve the classification of negativity preservers by combining recent advances in matrix analysis with some elementary arguments using well chosen test matrices. We unveil a complete analysis of the multi-variable setting with a striking combination of absolute monotonicity and single-variable rigidity appearing in our conclusions.
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关键词
transforms,matrices,tuples,negativity-preserving
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