[Gretl-users] Check for idempotent matrix in gretl

[Riccardo (Jack) Lucchetti]

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