> [!NOTE] Lemma > Let $n\geq 1.$ Let $\underline{v}\in \mathbb{R}^{n}$ be a [[Real n-Space|n-tuple of reals]]. Let $||\underline{v}||$ denote its [[Euclidean Norm|length]]. Then $||\underline{v}||\geq 0$with equality iff $\underline{v}$ is the [[Real Zero Vector|zero vector]]. **Proof**: We have $||\underline{v}||=\underline{v}\cdot \underline{v}$ thus the result follows from [[Dot Product is an Inner Product on Real n-Space|dot product is non-negative definite]].