Linear Algebra/Linear Dependance

Definition

We say that n vectors v₁ + ... + v_n are linearly dependent if there exist n coefficient ${\alpha }_1,\dots ,{\alpha }_n$, where at least one is different from null, whose linear combinations with the vectors yields the null vector:

${\alpha }_1{𝐯}_{\mathrm{𝟏}}+\cdots +{\alpha }_n{𝐯}_{𝐧}=O$

If such coefficients do not exist, the vectors are said to be linearly independent.