Basis (linear algebra)

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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 = { v1, …, vn } 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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