The Empty Set is Linearly Independent

Last updated Nov 1, 2022

Let $V$ be a Vector Space. Then $\emptyset \subset V$ is Linearly Independent.

Vacuously, there is no finite subset of $\emptyset$ so that there exists a nontrivial Linear Combination that equals $\mathbf{0}$. Thus $\emptyset$ is Linearly Independent. $\blacksquare$