Re: [Gretl-users] Check for idempotent matrix in gretl
On Fri, April 13, 2007 21:38, Allin Cottrell wrote:
On Fri, 13 Apr 2007, Andreas Karlsson wrote:
> Could you please add a check for idempotency in matrix? So that
> for a matrix, when one chooses Prpoerties > View the output
> tells if the matrix is idempotent, just as it now tells if it is
> e.g. square, symmetric or positive definite.
Yes. Since we calculate the eigenvalues anyway, I suppose we
could use them to check for idempotence. Can anyone remind me how
that would go (in the general case, allowing for asymmetry)?
Thanks.
The eigenvalues of idempotent matrices (in the symmetric case) can only
be 0 or 1. The thing is, I'm not sure if the converse holds: if a matrix
is symmetric and its eigenvalues are all 0 or 1, does that mean that it's
idempotent? My gut feeling is that the answer is yes, but I need to think
about it, it's not obvious.
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Facoltà di Economia "G. Fuà"
Ancona