Vector/Linear form/Zero test/Fact

Let ${\displaystyle {}V}$ denote a ${\displaystyle {}K}$-vector space and let ${\displaystyle {}v\in V}$ be a vector different from ${\displaystyle {}0}$.

Then there exists a

linear form ${\displaystyle {}f\colon V\rightarrow K}$ such that

${\displaystyle {}f(v)\neq 0}$.