Why is the geometric multiplicity more or equal to 1?

[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!

 

[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.

 

[Mark44]

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?

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.