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 $V$, respectively. These space have their natural and unique topologies arising from the operator norm on $L(V)$.

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