The Gau-Wang-Wu conjecture on partial isometries holds in the 5-by-5 case

Abstract

Gau, Wang and Wu in their LAMA'2016 paper conjectured (and proved for $n\leq 4$) that an $n$-by-$n$ partial isometry cannot have a circular numerical range with a non-zero center. We prove that this statement holds for $n=5$.