The quantum way to diagonalize hermitean matrices

An entirely quantum mechanical approach to diagonalize hermitean matrices has been presented recently. Here, the genuinely quantum mechanical approach is considered in detail for (2x2) matrices. The method is based on the measurement of quantum mechanical observables which provides the computational resource. In brief, quantum mechanics is able to directly address and output eigenvalues of hermitean matrices. The simple low-dimensional case allows one to illustrate the conceptual features of the general method which applies to (NxN) hermitean matrices.