On low-dimensional partial isometries

Qixiao He, Ilya M. Spitkovsky, Ibrahim Suleiman

Published 2022-06-05Version 1

Two statements concerning $n$-by-$n$ partial isometries are being considered: (i) these matrices are generic, if unitarily irreducible, and (ii) if nilpotent, their numerical ranges are circular disks. Both statements hold for $n\leq 4$ but fail starting with $n=5$.