2017
DOI: 10.48550/arxiv.1708.05777
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Connecting Commuting Normal Matrices

Fredy Vides

Abstract: In this document we study the local path connectivity of sets of m-tuples of commuting normal matrices with some additional geometric constraints in their joint spectra. In particular, given ε > 0 and any fixed but arbitrary m-tuple X ∈ Mn(C) m in the set of m-tuples of pairwise commuting normal matrix contractions, we prove the existence of paths between arbitrary m-tuples in the intersection of the previously mentioned sets of m-tuples in Mn(C) m and the δ-ball B ð (X, δ) centered at X for some δ > 0, with r… Show more

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