[Gretl-users] Re: Idempotency of residual maker matrix

On Mon, 11 Jan 2021, Alecos Papadopoulos wrote: > gretl 2020e Windows 64 > > I created a "residual maker" matrix M = I - X*inv(X'X)*X', which is > symmetric, non-invertible and  idempotent. Below I have copied its > properties as printed out by gretl. It clearly states that the matrix > is "Not idempotent". > > But It is, in theory and it is in practice: I performed the operation > M*M - M, and I got a matrix with zeros or numbers raised to the > 10^{-16} or even smaller. > > *What does it take for gretl to characterize a matrix as idempotent?* You're right, we were not taking finite precision into account. Here's a minimal script for creating a falsely not idempotent matrix: <hansl> set seed 123 n = 10 k = 3 X = mnormal(n, k) M = I(n) - qform(X, invpd(X'X)) </hansl> I just committed to git a fix which seems to work. @Allin: my fix changes the signature of a libgretl function; I'm fairly confident I ran all the checks so it doesn't break anything, but please review. -------------------------------------------------------   Riccardo (Jack) Lucchetti   Dipartimento di Scienze Economiche e Sociali (DiSES)   Università Politecnica delle Marche   (formerly known as Università di Ancona)   r.lucchetti(a)univpm.it   http://www2.econ.univpm.it/servizi/hpp/lucchetti ------------------------------------------------------- _______________________________________________ Gretl-users mailing list -- gretl-users(a)gretlml.univpm.it To unsubscribe send an email to gretl-users-leave(a)gretlml.univpm.it Website: https://gretlml.univpm.it/postorius/lists/gretl-users.gretlml.univpm.it/