Although the tridiagonal form found in (tridimat) is interesting in its own right, the more important result contained in (inverse4) is the fact that this analysis has resulted in a decomposition in terms of orthogonal (rather than merely conjugate) vectors. This result allows us to obtain the resolution matrix quickly for the model space from this form. In particular, if we define the diagonal matrix
D_G = G_n^TG_n, we see that
M^TM G_nD_G^-1T_nD_G^-1 G_n^T, and therefore, since
_model (M^TM)^ M^TM = M^TM(M^TM)^, we find easily that
_model = G_nD_G^-1G_n^T = _i=1^n g_ig_i^T (g_i,g_i).