Basis (linear algebra)

Definition

In mathematics, a set B of elements of a vector space V is called a basis if every element of V can be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called basis vectors.

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(0,1)-matrix Abelian group Abstract index notation Adjugate matrix Aequationes Mathematicae Affine connection Affine coordinate system Affine frame Affine geometry Affine group Affine space Affine transformation Albert Einstein Aleksandr Gorban Aleph-nought American Mathematical Society Angular momentum Antihermitian matrix Antisymmetric tensor August Ferdinand Möbius Augustin-Louis Cauchy Axiom of choice Baire category theorem Banach space Basic Linear Algebra Subprograms Basis (disambiguation)Basis of a linear program Basis of a matroid Basis transformation matrix Bernard Bolzano Bernhard Riemann Bernstein polynomial Bivector Block matrix Canonical basis Cardinal number Cardinality Carl Friedrich Gauss Cartan formalism (physics)Cartesian coordinate system Cartesian frame Category of vector spaces Cauchy stress tensor Cauchy–Binet formula Cayley–Hamilton theorem Change of basis Characteristic polynomial Chebyshev polynomials Cholesky decomposition Circulant matrix Classical treatment 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