Linear Independence

Definition. An indexed set of vectors $\{ v_1,v_2,\dots,v_p \}$ is said to be linearly independent, if the vector equation

$$x_1v_1+x_2v_2+\dots+x_pv_p=0$$

has only trivial solution, i.e. $x_i=0$. Otherwise, these vectors are said to be linearly dependent.