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In linear algebra, a basis is a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space or free module, or, more simply put, a "coordinate system".^{[1]} In more general terms, a basis is a linearly independent spanning set.
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Definition
A basis B of a vector space V over a field F is a linearly independent subset of V that spans (or generates) V.
In more detail, suppose that B = { v_{1}, …, v_{n} } is a finite subset of a vector space V over a field F (such as the real or complex numbers R or C). Then B is a basis if it satisfies the following conditions:
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