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basis


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A set S of vectors is a spanning set if any vector can be written as a linear combination of those in S. If, in addition, the vectors in S are linearly independent, then S is a basis. It follows that any vector can be written uniquely as a linear combination of those in a basis. In 3-dimensional space, any set of three non-coplanar vectors u, v, w is a basis, since any vector p can be written uniquely as p=xu+yv+zw. In 2-dimensional space, any set of 2 non-parallel vectors has this property and so is a basis. Any one of the vectors in a set currently being taken as a basis may be called a basis vector.

Subjects: Mathematics.


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