Definition:Trivial Norm/Vector Space

Definition
Let $\left({K, +, \circ}\right)$ be a division ring endowed with the trivial norm.

Let $V$ be a vector space over $K$, with zero $0_V$.

Then the map $\left\Vert{\cdot}\right\Vert: V \to \R_+ \cup \{0\}$ given by:


 * $\left\Vert{x}\right\Vert = \begin{cases}

0 & : \text{if $x = 0_V$}\\ 1 & : \text{otherwise} \end{cases}$

defines a norm on $V$, called the trivial norm.

Also see

 * Trivial Norm on Vector Space is Norm