Numerical radius
= Numerical radius
{title2=$w(T)=\sup_{\|u\|=1}|\langle Tu,u\rangle|$}
{wiki=Numerical_range\#Numerical_radius}
For a bounded <linear operator> on a complex <Hilbert space>, the numerical radius is the supremum of the absolute values in its <numerical range of an operator>. It is a <norm> equivalent to the <operator norm>, with $w(T)\leq\|T\|\leq2w(T)$. For a self-adjoint operator the two <norms> agree.