i think the "inverting by partitioning" from chap.2.7. doesnt let me benefit well from the SVD advantages.
i guess its not a implementations fault of me, but something systematic.

small description of my proble.

i try to solve a system of size >100x100 but the matrix is a double bordered block diagonal.
so i can invert well the P part cos are all samll 7x7 mats
the R part is Q.transp()
and the S part is of size 3x3
but in the end Rinv is not equal Qinv.transp()
and if i solve the whole system in one the matrix i get isnt nearly the same as the block inverted one. they are simmilar but the block one doesnt solve very well.

its all a numerical problem
it seams that i cannot use block invert with SVD cos its all to close to zero.
i have a 100x100 matrix but it has just rank of about 60