Dot Product of Vector with Itself

Theorem
Let $\mathbf u$ be a vector in the real Euclidean space $\R^n$.

Then:
 * $\mathbf u \cdot \mathbf u = \norm {\mathbf u}^2$

where $\norm {\mathbf u}$ is the length of $\mathbf u$.

Also presented as
This can also be seen presented as:
 * $\norm {\mathbf u} = \paren {\mathbf u \cdot \mathbf u}^{1/2}$

or:


 * $\norm {\mathbf u} = u = \sqrt {\mathbf u \cdot \mathbf u}$

and so on.