Definition:Equivalence of Norms

Definition
Let $\|\cdot\|_1$ and $\|\cdot\|_2$ be norms on a vector space $V$.

$\|\cdot\|_1$ and $\|\cdot\|_2$ are equivalent if there are real constants $c$ and $C$ such that $c\|x\|_1 \leq \|x\|_2 \leq C\|x\|_1$ for all $x \in V$.