Let $\left(\mathbf{v}_1, \ldots, \mathbf{v}_n\right)$ be any orthonormal basis of $\mathbb{R}^n$. Show that $$\mathbb{I}_n = \sum_{k=1}^n \mathbf{v}_k \mathbf{v}_k^T.$$
Let $\left(\mathbf{v}_1, \ldots, \mathbf{v}_n\right)$ be any orthonormal basis of $\mathbb{R}^n$. Show that
$$\mathbb{I}_n = \sum_{k=1}^n \mathbf{v}_k \mathbf{v}_k^T.$$