A complex number z ∈ C {\displaystyle {}z\in \mathbb {C} } defines a homothety μ z : v → z v {\displaystyle {}\mu _{z}\colon v\rightarrow zv} on C n {\displaystyle {}\mathbb {C} ^{n}} . For what numbers z {\displaystyle {}z} is this an isometry, a self-adjoint endomorphism, a normal endomorphism?
