I need to plot the phase portrait of the following gradient system, $x'=-\nabla V$.
$$V=x^2+y^2$$
Here are my workings so far,
$$x'=-\nabla V = \begin{bmatrix}-2x \\ -2y \end{bmatrix} = \begin{bmatrix}-2 & 0 \\ 0 & -2\end{bmatrix} \begin{bmatrix}v_1 \\ -v_2 \end{bmatrix}= \begin{bmatrix}0 \\ 0 \end{bmatrix}$$
$\lambda ^2+4\lambda+4=0$
$\lambda=-2,-2$
But how do I find the fixed points and draw the phase portrait?