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arXiv · 2310.07196

Norms on complex matrices induced by random vectors II: extension of weakly unitarily invariant norms

Ángel Chávez·Stephan Ramon Garcia·Jackson Hurley
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Abstract

We improve and expand in two directions the theory of norms on complex matrices induced by random vectors. We first provide a simple proof of the classification of weakly unitarily invariant norms on the Hermitian matrices. We use this to extend the main theorem in [7] from exponent $d\geq 2$ to $d \geq 1$. Our proofs are much simpler than the originals: they do not require Lewis' framework for group invariance in convex matrix analysis. This clarification puts the entire theory on simpler foundations while extending its range of applicability.

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Ángel Chávez, Stephan Ramon Garcia, Jackson Hurley. 2023-10-11. Norms on complex matrices induced by random vectors II: extension of weakly unitarily invariant norms. https://arxiv.org/abs/2310.07196

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