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arXiv · 1409.1905

Unitary equivalence of normal matrices over topological spaces

Greg Friedman·Efton Park
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Abstract

Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point of X. We use obstruction theory to establish a necessary and sufficient condition for A and B to be unitarily equivalent. We also determine bounds on the number of possible unitary equivalence classes in terms of cohomological invariants of X.

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Greg Friedman, Efton Park. 2014-09-05. Unitary equivalence of normal matrices over topological spaces. https://arxiv.org/abs/1409.1905

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