Continuous spectrum- and commutativity-preserving maps on normal matrices with spectra in a given interval image are conjugations, transpose conjugations, or spectrum orderings with fixed eigenspaces.
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The combinatorics of permuting and preserving curve-bound spectra
Continuous spectrum- and commutativity-preserving maps on normal matrices with spectra in a given interval image are conjugations, transpose conjugations, or spectrum orderings with fixed eigenspaces.