Mathematics — Linear Algebra · self-adjoint-operators
Problem
Fix u,x∈V. Define T∈L(V) by Tv=⟨v,u⟩x for every v∈V.
(a) Prove that if V is a real vector space, then T is self-adjoint if and only if the list u,x is linearly dependent.
(b) Prove that T is normal if and only if the list u,x is linearly dependent.