Re: [eigen] [patch] LDLt decomposition with rank-deficient matrices

[FMDSPAM <fmdspam@xxxxxxxxx>]

Hi Experts,

please, for my personal clarification, let me ask:
(I'm not asking for a brief lesson in lin alg. but I have to happily 
live with those answers :-) )

Def.:
    D_labil := "how many zeros in vectorD()"
    D_instable : "how many entries in vectorD() are smaller or equal 0.0"

a) LDLt for non singular matrix is rank-revealing (of course, i hope), 
n_labil = 0
b) LDLt for positive definite matrix => D_instable = 0

c) LDLt for singular matrix is not rank-revealing, but: n_deficit > 0
d) LDLt for indefinite matrix => D_instable > 0  but counting D(i) <= 
0.0 is meaning less?

e) Do all this also hold for LLt decompositions?

Regards
Frank