[:linear basis:]
• A *linear basis* is a set of vectors $V$ in a linear space which are linearly independent and whose span is $V$
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• Fun basis facts, which are true in generic fields, not just $\mathbb R^n$
• Every linearly independent set of vectors can have vectors added to it to form a basis.
• Every set of vectors which spans a linear space can have vectors removed to form a basis.
• Bases all have the same cardinality
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