Eigenvalues and Eigenvectors

Walkthrough

Find the eigenvalues of A = [[3, 0], [0, 5]].

1. 1.Recall the method: eigenvalues λ satisfy the characteristic equation det(A − λI) = 0.
2. 2.Set up the characteristic equation: det([[3−λ, 0], [0, 5−λ]]) = 0.
3. 3.Compute the determinant: (3−λ)(5−λ) − 0 = (3−λ)(5−λ) = 0.
4. 4.Solve: λ₁ = 3 or λ₂ = 5.
5. 5.So the eigenvalues are 3 and 5. (Note: for a diagonal matrix, the eigenvalues are the diagonal entries.)