Assume that $V$  is  a  finite  dimensional real or complex  normed linear space. Let  $Iso(V)\subset GL(V)\subset L(V)$ be the space of linear isometric endomorphisms, invertible  endomorphism and linear endomorphisms on $V$. These space have their natural topologies,

>Is $Iso(V)$  a  deformation retract of $GL(V)$?