Proof of Böttcher and Wenzel’s conjecture on commutator norms for 3-by-3 matrices

doi:10.1016/j.laa.2006.11.021

Linear Algebra and its Applications

Volume 422, Issues 2–3, 15 April 2007, Pages 659-663

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Abstract

Böttcher and Wenzel conjectured that the Frobenius norm of the commutator of two real matrices of Frobenius norm 1 is at most $\sqrt{2}$ and proved this for 2-by-2 matrices. In this paper, the conjecture is proved for 3-by-3 matrices.

AMS classification

15A60

15A45

65F35

Keywords

Commutator

Frobenius norm

Kronecker product

Sum of squares