Re: [Gretl-users] Check for idempotent matrix in gretl
On Fri, April 13, 2007 23:17, Riccardo (Jack) Lucchetti wrote:
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.
Thinking a bit more about it, I thought it would be way more economical,
from a computational viewpoint, to decide whether a matrix is idempotent
or not simply by a multiplication check, because matrix multiplication is
much cheaper than the eigenproblem. But, may I ask what this check is
for?
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Facoltà di Economia "G. Fuà"
Ancona