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Real Linear Combinations
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Real Subspaces
Real Vector Bases
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Real Vectors Span


The span of a finite set of vectors $v_1, \dots , v_k \in \R ^n$ is the set of all linear combiniations of the vectors $v_1, \dots , v_k$.

More generally, given a set $A \subset \R ^n$ the span of $A$ is the set of all linear combinations formed from finite subsets of $A$. This is sometimes also called the linear hull of $A$.

The span of a set of vectors is a subspace.


We denote the span of $v_1, \dots , x_k \in \R ^d$ by

\[ \span(\set{v_1, \dots , v_k}) \]

Other notation in use, in particular when we are dealing with the span of a set $A \subset \R ^d$ is $\lin A$.

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