- #26

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Sorry you are right, it was my faultit is quite rare that ##Q## and ##P## commute

Trying again: the permutation matrix ##P## needed to reorder ##A## eigenvalues has the special property ##P=P^T=P^{-1}##.

##E=PE_1P##, ##E_1## is the ##A## eigenvalues diagonal matrix ##E## reordered with its ##k## possibly zero eigenvalues as last ##k## entries.

it turn out the following:

##A=QEQ^T##

##A=QPE_1PQ^T##

##PAP^T=PQPE_1PQ^TP^T=PQPE_1P^TQ^TP^T=(PQP)E_1(PQP)^T##

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