1. The problem statement, all variables and given/known data Vectors I1> and I2> create the orthonormal basis. Operator O is: O=a(I1><1I-I2><2I+iI1><2I-iI2><1I), where a is a real number. Find the matrix representation of the operator in the basis I1>,I2>. Find eigenvalues and eigenvectors of the operator. Check if the eigenvectors are orthonormal. 2. Relevant equations Av=λv 3. The attempt at a solution My problem is concerning the first part of this excercise. I'm not really familiar with this notation of the operator and not sure how I should get the matrix. I have tried improvisation and got the matrix 2a^2 -2a^2 -2a^2 2a^2 When I tried to calculate eigenvalues, I didn't get anything reasonable, so I believe that my matrix is wrong. Please help me regarding this problem, once I have the right matrix I will not have the problem finding eigenvalues nor eigenvectors.