# [SciPy-user] det(A-\lambda B) is identically zero

Pearu Peterson pearu at scipy.org
Fri Feb 13 07:56:15 CST 2004

On Fri, 13 Feb 2004, Nils Wagner wrote:

> Please find attached a small example for a singular pencil
> A-\lambda B. det(A-\lambda B) is identically zero.
> However linalg.eig(A,B) computes certain eigenvalues.

And one of them is inf. That should make an user careful
when manipulating with (A,B) eigendata.

> although \lambda can be chosen arbitrarely.

Well, if lambda is small then det is close to small number indeed.
However note that

>>> linalg.det(A-1e5*B)
-966.29150970670446

for instance.

> There should be at leat a warning in such a case.

I think it is a computer numerics issue rather than of scipy.
What would be the criterion when such a message should be displayed?

Pearu