# basis

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## basis

Maths (of a vector space) a maximal set of linearly independent vectors, in terms of which all the elements of the space are uniquely expressible, and the number of which is the dimension of the space

## Basis

in mathematics, a set of linearly independent vectors taken in a certain order and plotted from a common origin. For vectors in three-dimensional space, any set of three vectors that are not parallel to the same plane can be used as a basis. If the vectors making up the basis are mutually orthogonal, then the basis is said to be orthogonal; if the vectors are of unit length, then the basis is an orthonormal basis. In the general case of an n-dimensional vector space, any set of n linearly independent vectors can be taken as a basis.

## basis

[′bā·səs]
(mathematics)
A set of linearly independent vectors in a vector space such that each vector in the space is a linear combination of vectors from the set.
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