Why is MATLAB giving me these weird eigenvectors? I am doing a problem which involves finding the eigenvalues and eigenvectors of the matrix $$
M=\begin{bmatrix}
0 & 1/2 & 1/2 \\
1/2 & 0 & 1/2 \\
1/2 & 1/2 & 0
\end{bmatrix}$$
When I compute by hand, I get eigenvalues of 1, -1/2, -1/2 with corresponding eigenvectors $\begin{bmatrix}1\\1\\1\end{bmatrix},\begin{bmatrix}-1\\1\\0\end{bmatrix},\begin{bmatrix}-1\\0\\1\end{bmatrix}$, but when I try to compute in MATLAB I get 
>>[A B] = eig(M)

A =

   -0.7152    0.3938    0.5774
    0.0166   -0.8163    0.5774
    0.6987    0.4225    0.5774


B =

   -0.5000         0         0
         0   -0.5000         0
         0         0    1.0000

The last eigenvector makes sense, but the first two aren't scalar multiples of the ones I got, which I figured they should be. Why are these also eigenvectors?

The eigenvectors are normalized to have a norm of 1 and are chosen to be orthogonal. They will be unique (up to scalar multiplication) only if they have different eigenvalues.
Here you have two eigenvectors that share the same eigenvalue.
