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arXiv · 2503.00451

On Moment-Entropy inequalities in the space of matrices

Dylan Langharst
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Abstract

In a series of works, Lutwak, Yang and Zhang established what could be called affine information theory, which is the study of moment-entropy and Fisher-information-type inequalities that are invariant with respect to affine transformations for random vectors. Their set of tools stemmed from sharp affine isoperimetric inequalities in the $L^p$ Brunn-Minkowski theory of convex geometry they had established. In this work, we generalize the affine information theory to the setting of matrices. These inequalities on the space of $n\times m$ matrices are induced by the interaction between $\mathbb{R}^n$ with its Euclidean structure and $\mathbb{R}^m$ equipped with a pseudo-norm.

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Dylan Langharst. 2025-03-01. On Moment-Entropy inequalities in the space of matrices. https://arxiv.org/abs/2503.00451

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