The normalized numerical range and the Davis-Wielandt shell

Brian Lins, Ilya M. Spitkovsky, Siyu Zhong

For a given $n$-by-$n$ matrix $A$, its {\em normalized numerical range} $F_N(A)$ is defined as the range of the function $f_{N,A}\colon x\mapsto (x^*Ax)/(\norm{Ax}\cdot\norm{x})$ o…