OK, so I've been there before, Hilbert Space that is. You know, infinite dimensional function space. At least I thought I had, that is untill I started reading A Hilbert Space Problem Book by Halmos. So operator theory, right. What's are bilinear, sesquilinear, conjugate linear, ect. - functionals or forms? What's a quadradic form? Someone, anyone, please help me: I'm lost in Hilbert Space. Edit:I understand inner product spaces, are these things definable in such terms?