Linear Independence

Definition

Let

• $V$ : Vector space
• $S=\{{\mathbf{v}}_1,{\mathbf{v}}_2,\dots ,{\mathbf{v}}_3\}$ : Set of two or more vectors in $V$

If no vectors in $S$ can be expressed as a linear combination of the others

Then we say $S$ is a linearly independent set

Otherwise, we say $S$ is linearly dependent