PowerPoint Presentation - 19th century in the the context of the 20th

Projection of OI solution on eigenvectors of C (EOFs)

C = EDET

T = Ea

For simplicity: H = I, R = rI, T := T-TB

Then a = D(D+R)-1ETTo

D(D+R)-1 = diag[ di/(di+r) ], ao=ETTo

Therefore ai/ao = di/(di+r)

In many applications (for spectrally red signals) diagonal elements of this matrix decrease from ~1 to ~0. In effect, the solution is constrained to the subspace spanned by the patterns with di>>r.