Definition:Square of Vector Quantity

Definition
Let $\mathbf u$ be a vector.

Let $\mathbf u \cdot \mathbf u$ denote the dot product of $\mathbf u$ with itself.

Then $\mathbf u \cdot \mathbf u$ can be referred to as the square of $\mathbf u$ and can be denoted $\mathbf u^2$.

Also known as
The square of $\mathbf u$ is also seen referred to as the self-product of $\mathbf u$.

Also see

 * Dot Product of Vector with Itself, demonstrating that $\mathbf u^2 = u^2$, where $u$ denotes the magnitude of $\mathbf u$.