# Vector space/Basis/Definition

Basis

Let be a
field,
and let be a
-vector space.
Then a
linearly independent
generating system
, ,
of is called a * basis* of .

Basis

Let ${}K$ be a
field,
and let ${}V$ be a
${}K$-vector space.
Then a
linearly independent
generating system
${}v_{i}\in V$, ${}i\in I$,
of ${}V$ is called a * basis* of ${}V$.