A [[Linear Subspace]] of [[Dimension|dimension]] $n$ is a [[Subset]] of a $n$-dimensional [[Vector Space|linear space]] 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]]