- #1

eherrtelle59

- 25

- 0

If I remember correctly, I should be able to look at certain 2 by 2 matrices and practically write down the eigenvalues and eigenvectors.

For example, I have a diagonal matrix, I know immediately what the eigenvalues and eigenvectors are.

E.g. M = \begin{bmatrix}

1 &0 \\[0.3em]

0 & x \\[0.3em]

\end{bmatrix}

Well, I know immediately λ_1 =1, λ_2 = x and that the eigenvectors are e_1 = (1 0) and e_2 = (0 1).

Now, what about an upper diagonal matrix?

Take M = \begin{bmatrix}

-1 & -1 \\[0.3em]

0 & x-(1/4) \\[0.3em]

\end{bmatrix}

I can see λ_1=1 and that e_1 = (1 0)

How do you find the second eigenvalue and eigenvector?