Hey guys, I am wondering if the following relationships hold for all operators A, regardless of whether they are linear or non-linear. A-1A = AA-1 = I [A,B] = AB - BA A|an> = λn|an>, where n ranges from 1 to N, and N is the dimension of the vector space which has an orthogonal basis |an>. Just one other question. Which is the more general definition of the adjoint (hermitian conjugate) A† of an operator A: (v, Au) = (A†v, u) or A† = (A*)T? I think it's the first one. The second one is a special case of the first which is valid if the vectors v and u are matrices. Your thoughts? Let's see if you can make a dumbass like me learn some maths!