@AndrewSalmon My math assignment is the following:
Assume that a 3x3 matrix A, has the eigen-values \lambda_1 = 1, \lambda_2 = 0.8 and \lambda_3 = 0.6 and the eigen-vectors:
$
v_1 = \begin{pmatrix}
1 \\
0 \\
2 \\
\end{pmatrix}
$
$
v_2 = \begin{pmatrix}
2 \\
3 \\
1 \\
\end{pmatrix}
$
$
v_3 = \begin{pmatrix}
0 \\
2 \\
1 \\
\end{pmatrix}
$
Every 3-vector $v$ can be written as a linear combination $v = x_1v_1 + x_2v_2 + x_3v_3$
What happens to $A^nv$ when $n \to \infty. What does that even mean?
