Ang. Re: [Gretl-users] Check for idempotent matrix in gretl
On Fri, April 13, 2007 23:17, Riccardo (Jack) Lucchetti wrote:
[...]
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?
Idempotent matrices play an essential role for the conditions under which a
quadratic form in normal variates has a chisquared distribution. See
Chapter 10.4 in James R. Schott (2005), Matrix Analysis for Statistics,
2nd. ed. Hoboken, NJ: Wiley.
On checking the idempoteny, I just thought of using a multiplication check.
Best regards,
Andreas