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The 33 pages that link to Basis (linear algebra), each with the reason it gives.

• Coordinate systemRelated: Basis vectors provide the directions used to express points and vectors numerically.

• Vector spaceRelated: A basis gives coordinates for every vector through unique linear combinations.

• Vector fieldRelated: A basis supplies the component directions used to describe each field vector.

• Linear algebraRelated: A basis gives coordinates for every vector in a space.

• Quantum superpositionRelated: A superposition is expressed as components relative to a chosen basis of states.

• Field extensionRelated: A basis over the base field counts the independent directions in the extension.

• VectorRelated: A basis gives each vector a unique set of coordinates in its space.

• Linear independenceRelated: Every basis is independent, and independence helps distinguish a basis from a redundant spanning set.

• Linear combinationRelated: A basis gives each vector a unique linear-combination representation.

• Rank–nullity theoremRelated: Extending a kernel basis supplies the vectors whose images form a basis of the image.

• TensorRelated: A basis lets a tensor be represented by components without defining the tensor itself.

• Dual spaceRelated: A basis lets functionals be specified by their values on basis vectors.

• Coordinate transformationRelated: A basis determines the component coordinates used to represent each vector.

• Linear mapRelated: A linear map is determined completely by its values on a basis.

• Linear operatorRelated: Choosing bases turns a linear operator into a matrix representation.

• EigenvectorRelated: Eigenvectors form a basis when the transformation can be diagonalized.

• Quotient spaceRelated: A basis adapted to W makes the surviving quotient directions visible.

• Rank (linear algebra)Related: A basis of either matrix space has as many elements as the matrix’s rank.

• Scalar multiplicationRelated: Scaling basis vectors helps express how linear maps act on the whole space.

• LatticeRelated: The chosen basis vectors generate every lattice point.

• Linear functionalRelated: A functional is determined by its values on any basis.

• Bilinear formRelated: Values on pairs of basis vectors determine the form everywhere by bilinearity.

• Finite-dimensional vector spaceRelated: A finite basis is the defining feature of this concept.

• Vector (physics)Related: A basis supplies the independent directions used to represent vector components.

• Column spaceRelated: A basis chosen from the columns gives a compact description of the column space.

• Euclidean vectorRelated: A basis lets vectors be expressed using coordinates without changing their geometric identity.

• Fundamental theorem of linear algebraRelated: Bases make the dimensions in the theorem countable.

• Vector notationRelated: Vector components are coefficients relative to a basis.

• Dimension theorem for vector spacesRelated: A kernel basis extended to a domain basis yields the theorem’s dimension count.

• Family (mathematics)Related: A basis is often indexed to specify coordinates and organize its vectors.

• Steinitz exchange lemmaRelated: Exchanging vectors until the independent set is included yields the finite-dimensional basis theorem.

• Two-dimensional spaceRelated: Two basis directions provide independent ways to reach every point in a plane.