# Definition A *vector subspace* of a [[Vector Space]] $V$ is a subset of $V$ that is itself a [[Vector Space]]. Any set of vectors $\{\pmb{y}_i i = 1, m\}$ is said to *generate* a subspace of $V$ which is formed by all possible linear combinations of the form: $a_1 \pmb{y}_1 + a_2 \pmb{y}_2 + \ldots a_m \pmb{y}_m$