Linked from

The 56 pages that link to Vector space, each with the reason it gives.

• Coordinate systemNarrower topic: Coordinates represent vectors in a chosen basis, while the vector space exists independently of that basis.

• EigenvalueNarrower topic: Eigenvalues and eigenvectors are defined for linear maps on vector spaces.

• Convex setNarrower topic: The definition uses real scalar combinations of points.

• Euclidean distanceNarrower topic: Difference vectors belong to a vector space, where norms can measure their length.

• Cauchy–Schwarz inequalityNarrower topic: The inequality applies to vectors in spaces with a suitable inner product.

• Affine transformationNarrower topic: The linear part of an affine map acts on the displacement vectors of its domain.

• Basis (linear algebra)Narrower topic: A basis is defined relative to the space it spans.

• Inner productNarrower topic: Inner products are defined on vector spaces and interact with their linear structure.

• VectorNarrower topic: Vectors are the elements of this structure, which generalizes arrows beyond physical space.

• Homogeneous coordinatesNarrower topic: Homogeneous tuples are nonzero vectors, and their scalar multiples encode one projective point.

• Linear independenceNarrower topic: Linear independence is defined for vectors drawn from a common vector space.

• Quadratic formNarrower topic: Quadratic forms assign values to vectors in a vector space.

• Linear combinationNarrower topic: Linear combinations are defined for elements of a vector space.

• Normed vector spaceNarrower topic: The normed structure adds a size function to this algebraic foundation.

• Vector additionNarrower topic: Its axioms state the general rules that vector addition obeys.

• Lie algebraNarrower topic: A Lie algebra’s elements and linear combinations live in this underlying structure.

• Rank–nullity theoremNarrower topic: The domain and codomain must be vector spaces for the theorem’s dimension statement.

• TensorNarrower topic: Tensors are defined from vector spaces and their duals.

• Dual spaceNarrower topic: A dual space is defined from a vector space and inherits its scalar field.

• Affine spaceNarrower topic: The associated vector space supplies the differences between affine points.

• Group representationNarrower topic: The representation acts on this space through invertible linear transformations.

• Coordinate transformationNarrower topic: Linear coordinate transformations are defined through representations of vectors in vector spaces.

• Linear mapNarrower topic: Linear maps are defined between vector spaces and preserve their two operations.

• Linear operatorNarrower topic: Linear operators take vector spaces as their domains and codomains.

• Invariant subspaceNarrower topic: A subspace is defined inside a vector space.

• Projective spaceNarrower topic: The lines used to define projective points lie in a vector space.

• EigenvectorNarrower topic: Eigenvectors and their spans are defined within vector spaces.

• Inner product spaceNarrower topic: Inner product spaces add a geometric pairing to this underlying algebraic structure.

• Quotient spaceNarrower topic: Both the ambient space and its quotient carry vector-space structure.

• Affine combinationNarrower topic: Vector-space operations supply the addition and scalar multiplication used in affine combinations.

• Kernel (linear algebra)Narrower topic: The kernel is a subspace of the transformation’s vector-space domain.

• Rank (linear algebra)Narrower topic: Row and column spaces are subspaces whose dimensions define rank.

• Scalar multiplicationNarrower topic: Scalar multiplication is one of the operations that defines a vector space.

• Eigenvalue problemNarrower topic: Eigenvectors and operator actions are defined within vector spaces.

• Lie bracketNarrower topic: A Lie bracket takes two vectors from this underlying space and returns another.

• ElementNarrower topic: Its vectors are elements of the underlying set, with operations acting on them.

• Linear functionalNarrower topic: Its elements are the inputs a linear functional assigns scalars to.

• Finite-dimensional vector spaceNarrower topic: Finite-dimensional vector spaces are the vector spaces whose bases contain finitely many vectors.

• Geometric algebraNarrower topic: The algebra begins with vectors and extends their product structure.

• Parallelogram lawNarrower topic: The law compares sums and differences formed within a vector space.

• Affine subspaceNarrower topic: Its linear subspaces supply the directions that an affine subspace translates.

• Gaussian binomial coefficientNarrower topic: The objects being counted are its subspaces.

• Matrix theoryNarrower topic: Matrices represent maps between vector spaces, the setting behind their geometric meaning.

• Euclidean vectorNarrower topic: Euclidean vectors belong to a vector space, with an inner product adding geometric structure.

• Eigenvalues and eigenvectorsNarrower topic: Eigenvectors are nonzero elements of a vector space acted on by a linear map.

• Algebra over a fieldNarrower topic: An algebra is first a vector space, with multiplication added.

• Bra–ket notationNarrower topic: Kets obey vector addition and scalar multiplication.

• Dieudonné's theoremNarrower topic: The theorem lifts projective geometry back to transformations of these underlying spaces.

• Operator overloadingNarrower topic: Overloaded arithmetic notation can make vector operations resemble their abstract algebraic definitions.

• Steinitz exchange lemmaNarrower topic: The lemma applies to vectors and linear combinations within this algebraic structure.