Singular Values, Eigenvalues and Diagonal Elements Of The Commutator Of 2x2 Rank One Matrices

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Che-Man Cheng
Yaru Liang

Abstract

We determine the region of singular values of the commutator XY-YX for 2x2 rank one complex matrices X and Y. This answers in affirmative a conjecture raised in [Wenzel 2015] when 2x2 matrices are concerned. Our approach and proofs also lead to a complete relation between the singular values, eigenvalues and diagonal elements of the commutator under consideration.

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