
454 D.T.M. Slock
Then we get from (13)-(16)
R~ry = LHD-1L = L'HL"HD"-IL "L' =~ L = L"L' , D = D" (17)
by uniqueness of UDL triangular factorizations.
If the matrix Ryy is singular, then there exist linear relationships between certain
components of Y. As a result, certain components Yi will be perfectly predictible from
the previous components and their resulting orthogonalized version Yi will be zero. The
corresponding diagonal entry in D will hence be zero also. For the orthogonalization of the
following components, we don't need this yi. As a result, the entries under the