I'm in search of some informations (or good sources) about the formalism of pauli vectors; in particular i refer to any useful formulae like those shown in (Eigenvectors of Pauli vectors). Infact, i was asked to solve an excercise in which i would had to express a matrix in the basis that diagonalize another one, and i couldn't hold up with all that calculations (find eigenvalues, eigenvectors, the inverse of the eigenvectors matrix, ecc)... then, i was said that i should had used notorious facts about eigenvalues/eigenvectors of matrices expressible in terms of pauli matrices.. the problem is that i never knew about those facts, nor suggested book contains similiar informations. Moreover i wasn't able to find anything googling myself.. could anybody provide good sources about?
NOTE) I would appreciate a complete treatment of the above topics; for example in (Eigenvectors of Pauli vectors) there wasn't the general case of: $A=\alpha_0I+\vec{\alpha} \cdot \vec{\sigma}$