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
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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 Basisthat 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 Basiscan be taken as a basis.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.