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Basis (Linear Algebra)**

A basis of a vector space \((V,+,\cdot)\) over a field \(k\) is a subset \(S\subseteq V\) which is linearly independent and spans \(V\). In infinite dimensions, one specifies a difference between a 'Hamel basis' (using finite sums for linear independence and span) and a 'Schauder basis' (using convergent infinite sums for linear independence and span).