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, which define a "coordinate system" (as long as the basis is given a definite order).Halmos, Paul Richard (1987) Finite-dimensional vector spaces (4th edition) Springer-Verlag, New York, page 10, ISBN 0-387-90093-4 In more general terms, a basis is a linearly independent spanning set.
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