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Exists if a non-zero vector satisfies f(x) = λx.
A non-zero vector that satisfies f(x) = λx for some λ.
Equal to the kernel of f - λId_E.
The endomorphism f - λId_E is non-injective.
P_A(λ) = det(A - λI_n).
There exists a basis of eigenvectors for the matrix.
States that P_A(A) = 0 for the characteristic polynomial.
It can be expressed as A = PDP^(-1) for some diagonal D.
Its characteristic polynomial is factored over R.
Use A^k = P D^k P^(-1) if A is diagonalisable.