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arXiv · 2401.17863

Invariant embeddings and weighted permutations

Mitja Mastnak·Heydar Radjavi
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Abstract

We prove that for any fixed unitary matrix $U$, any abelian self-adjoint algebra of matrices that is invariant under conjugation by $U$ can be embedded into a maximal abelian self-adjoint algebra that is still invariant under conjugation by $U$. We use this result to analyse the structure of matrices $A$ for which $A^*A$ commutes with $AA^*$, and to characterize matrices that are unitarily equivalent to weighted permutations.

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Mitja Mastnak, Heydar Radjavi. 2024-01-31. Invariant embeddings and weighted permutations. https://arxiv.org/abs/2401.17863

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