This may be a very silly question, but still apologies, I read in Sheldon Axler, that the inner product of two orthogonal vectors is DEFINED to be 0. Let u,v belong to C^n. I am unable to find a direction of proof which proves that for an nth dimension vector space, if u perp. to v, then <u,v> = 0 Is it really just defined ? Or it can be proved to be 0 ?