Basis (linear Algebra)
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). In more general terms, a basis is a linearly independent spanning set.
Given a basis of a vector space, every element of the vector space can be expressed uniquely as a finite linear combination of basis vectors. Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space.
Read more about Basis (linear Algebra): Definition, Expression of A Basis, Properties, Examples, Extending To A Basis, Example of Alternative Proofs, Ordered Bases and Coordinates
Famous quotes containing the word basis:
“The basis of world peace is the teaching which runs through almost all the great religions of the world. “Love thy neighbor as thyself.” Christ, some of the other great Jewish teachers, Buddha, all preached it. Their followers forgot it. What is the trouble between capital and labor, what is the trouble in many of our communities, but rather a universal forgetting that this teaching is one of our first obligations.”
—Eleanor Roosevelt (1884–1962)