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