# Definition:Normed Vector Space

## Definition

Let $\struct {K, +, \circ}$ be a normed division ring.

Let $V$ be a vector space over $K$.

Let $\norm {\,\cdot\,}$ be a norm on $V$.

Then $\struct {V, \norm {\,\cdot\,} }$ is a normed vector space.

## Also known as

When $\norm {\,\cdot\,}$ is arbitrary or not directly relevant, it is usual to denote a normed vector space merely by the symbol $V$.

A normed vector space is also known as a normed linear space.

## Also see

• Results about normed vector spaces can be found here.