A newly developed approach based on the spectral decomposition principle, which is usefull in crystallography , is applied for the first time in this paper. The compliance fourth-rank tensor of crystalline media belonging to the monoclinic system is, thus, spectrally decomposed, its eigenvalues are evaluated, together with the elementary idempotent fourth-rank tensors, which decompose uniquely the fourth-rank tensor space into orthogonal subspaces. Accordingly, energy orthogonal states of stress and strain are derived from the idempotent tensors, namely eigenstates which do not perform work along the deformations produced by the others. [...] (From the abstract)