The dimension of a subspace is less than or equal to the dimension of the whole space

Created almost 9 years ago, updated about 8 hours ago

For $U\subseteq V$ with $V$ finite-dimensional, $\dim U\le\dim V$. A basis of $U$ is independent in $V$ and can be extended to a basis of $V$. Equality forces $U=V$. The equality conclusion is special to finite dimension.

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