Subspace Span

Last updated Nov 1, 2022

Let $V$ be a Vector Space on Field $F$. Let $S \subset V$. The Subspace Span of $S$ is $$\text{span} S = \bigcap\limits{W \subset V : S \subset W, W \text{ is a subspace of V}}$$ $\blacksquare$

1. The Subspace Span is a Vector Subspace since Intersection of Vector Subspaces is a Vector Subspace.
2. The Subspace Span is the Set of all Linear Combinations