A [[Linear Subspace]] of $\R^n$ is a [[Set]] of [[Vector|Vectors]] in $\R^n$ that is [[Closure|Closed]] under addition, subtraction, and [[Vector Arithmetic|Scalar Multiplication]]. Every [[Linear Subspace|Subspace]] $U\in \R^{n}$ has a [[Basis]], which is a [[Linear Independence|linearly independent]] [[Set|set]] of [[Vector|Vectors]] that [[Span|span]] $U$. >[!note] >All [[Linear Subspace|Linear Subspaces]] are an [[Infinite Set]], with the sole exception of the [[Zero Linear Subspace|Zero Space]]