Let $y_n = (y_{1n}, y_{2n})^T.$
I'm wondering what the condition on the matrix $A$ is for the recursive system of equations $$y_{n+1} = Ay_n$$ to be stable (i.e neither $y_1$ or $y_2$ blows up). Can I express this in eigenvalues somehow?
I'm specially interested in the $2\times 2$ case but maybe it generalizes to higher dimensions.