Proving kernel of matrix is isomorphic to 0 eigenvalue's eigenvectors

1. Sep 25, 2007

Coolphreak

1. The problem statement, all variables and given/known data
I want to prove that the eigenvectors corresponding to the 0 eigenvalue of hte matrix is the same thing as the kernel of the matrix.

2. Relevant equations
A = matrix.
L = lambda (eigenvalues)

Ax=Lx

3. The attempt at a solution

Ax = 0 is the nullspace.

Ax = Lx
Lx = 0.
L= 0.
the eigenvectors corresponding to the 0 eigenvalue are the same as the nullspace.

Is this a sufficient enough proof?

2. Sep 25, 2007

morphism

No, it's not. Maybe you have the right idea, but what you've written down doesn't make a lot of sense.

The nullspace is {x : Ax = 0}. Can you write down what the set of eigenvectors corresponding to zero is?

3. Sep 26, 2007

Coolphreak

Isn't the the set of eigenvectors which correspond to the 0 eigenvalue?

4. Sep 26, 2007

matt grime

What is the definition of the kernel of a matrix? What is the definition of the set of eigenvectors of a matrix with eigenvalue zero? Aren't they trivially the same?