# Definition If the basis generating the [[vector subspace]] has dimension $m$, and the [[vector space]] has dimension $n$, and we have $m < n$, then we say that the [[vector subspace]] is a *proper subspace* of the [[vector space]] (i.e. they are not [[Group Isomorphism|isomorphic]]). That is, the [[dimension]] of the [[vector subspace]] is smaller than that of the original [[vector space]] itself, and is entirely contained within it.