Linear independence and dependence

Abstract

A set of vectors E is said to be linearly dependent if there exist distinct vectors A₁,..., A _k in E and numbers a₁,...,a _k , not all zero, such that

$$ {a_1}{{\rm{A}}_1}{\rm{ }} + {\rm{ }}{a_2}{{\rm{A}}_2}{\rm{ }} + {\rm{ }}...{\rm{ }} + {\rm{ }}{a_k}{{\rm{A}}_k} = 0. $$

(*)

Equation (*) is called a linear relation between A₁,...,A _k .