Basis (linear Algebra)

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:

    Our fathers and grandfathers who poured over the Midwest were self-reliant, rugged, God-fearing people of indomitable courage.... They asked only for freedom of opportunity and equal chance. In these conceptions lies the real basis of American democracy. They and their fathers give a genius to American institutions that distinguished our people from any other in the world.
    Herbert Hoover (1874–1964)