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Apr 20'25

Exercise

[math] \newcommand{\mathds}{\mathbb}[/math]

Prove that for the usual matrices [math]A,B\in M_N(\mathbb C)[/math] we have

[[math]] \sigma^+(AB)=\sigma^+(BA) [[/math]]

where [math]\sigma^+[/math] denotes the set of eigenvalues, taken with multiplicities.