Homework Help: Why is the geometric multiplicity more or equal to 1?

1. Aug 14, 2012

Hernaner28

Hi. I've got a theoretical doubt: why is the geometric multiplicity more or equal to 1?

Couldn't happen that the eigenspace is the null vector?

Thanks!

2. Aug 14, 2012

Hernaner28

Oh no, it couldn't happen because when I get the eigenvalues I am getting those values for the corresponding vectors different to the null.

3. Aug 14, 2012

Staff: Mentor

An eigenvector is defined to be a nonzero vector x such that (A - λI)x = 0. The eigenspace is the space spanned by all of the eigenvectors. Since no eigenvector can be the zero vector, the eigenspace can't be just the space with 0 in it.