How to find the Glebsch Gordan coefficients by matrix form. Let's suppose we have a two spin 1/2 particles, we get that (check attachment 1). These are the corresponding coefficients the classic way. Now if I want find them the matrix way, where the matrix should be diagonalized. How do I proceed? So my question is how knowing the old basis and the new basis -how can we find the matrix containing the Glebsch Gordan coeficients? I would like to add the the matrix main operator should be either Jz or J^2, as far as I know. Please, correct me if I am wrong. Thanks!