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Lchan1
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Homework Statement
A Hermitian operator is such that, for arbitrary vectors ai and aj
in a vector space,we have (ai,Oaj) = (Oai, aj).
Prove that if for an arbitrary vector a in the vector space, the operator O satisfies
(a,Oa) = (Oa, a),
then O is Hermitian
Homework Equations
The Attempt at a Solution
Our prof gave us a hint:
let a=a1+z1a2 and a=a1+z2a2. and find the appropriate zs to satisfy the proof. I tried doing the inner product using the different a. and got myself no where.