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

[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?

[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?

[Coolphreak]

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

[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?