If $\|\mathbf{v}\| = 4,$ then find $\mathbf{v} \cdot \mathbf{v}.$
We have that $\mathbf{v} \cdot \mathbf{v} = \|\mathbf{v}\|^2 = \boxed{16}.$
We have that $\mathbf{v} \cdot \mathbf{v} = \|\mathbf{v}\|^2 = \boxed{16}.$
The final answer is $The final answer is $\boxed{16}$.$. I hope it is correct.