A subset  <i>S</i> of a vector space <i> V</i> is a linearly dependent set over  a field <i>F</i> if there are vectors <i>v<sub>1</sub>,...,v<sub>n</sub></i> from <i>S</i> 
and scalars 
 <i>a<sub>1</sub>, ..., a<sub>n</sub></i>
from <i>F</i>, not all 0, such that 
 <i>a<sub>1</sub>v<sub>1</sub>+...+a<sub>n</sub>v<sub>n</sub>=0</i>.