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 self ... might be regarded as a sort of citadel of the mind, fortified without and containing selected treasures within, while love is an undivided share in the rest of the universe. In a healthy mind each contributes to the growth of the other: what we love intensely or for a long time we are likely to bring within the citadel, and to assert as part of ourself. On the other hand, it is only on the basis of a substantial self that a person is capable of progressive sympathy or love.”
—Charles Horton Cooley (1864–1929)