I only know the definition of the tensor product of two vectors and was reading a text which concerned a function $u:\mathbb{R}^3 \to \mathbb{R}^3$ such that $|u| = 1$ and $u(x) = \frac{x}{|x|}$. The text claimed that
$$\nabla u = \frac{1}{|x|}\left(I-\frac{x}{|x|} \otimes \frac{x}{|x|}\right)$$
and therefore $|\nabla u|^2 = \frac{2}{|x|^2}$.
I have no idea how they actually arrived at the expression for $\nabla u$ and then how did they take the norm of $\nabla u$? Because isn't $\nabla u$ a $3 \times 3$ matrix so what matrix norm is being used?