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The 51 pages that link to Linear map, each with the reason it gives.

• EigenvalueNarrower topic: Eigenvalues describe how a linear transformation acts along special vector directions.

• Vector spaceRelated: Linear maps are the structure-preserving functions between vector spaces.

• DeterminantNarrower topic: A matrix represents a linear transformation whose volume scaling the determinant records.

• Jacobian matrixNarrower topic: A Jacobian acts as the linear map approximating a nonlinear function locally.

• Linear algebraRelated: Linear transformations are the structure-preserving maps at the heart of the subject.

• Affine transformationRelated: The linear part changes directions and scale before the translation shifts every point.

• Matrix multiplicationNarrower topic: Matrices represent linear transformations, and their product represents composition.

• Basis (linear algebra)Narrower topic: A transformation is represented by a matrix after bases are chosen in both spaces.

• Representation theoryRelated: Each represented group element or algebra element acts through a linear transformation.

• VectorRelated: It maps vectors while preserving the operations that define their structure.

• Rotation matrixNarrower topic: A rotation matrix is a coordinate representation of a linear transformation.

• Linear combinationRelated: It carries linear combinations to combinations with the same coefficients.

• Singular value decompositionNarrower topic: Geometrically, the decomposition describes how a linear map acts on orthogonal directions.

• Rank–nullity theoremNarrower topic: The theorem applies to linear maps between finite-dimensional spaces.

• Dual spaceRelated: Linear functionals are linear maps with a one-dimensional codomain.

• Identity matrixRelated: The identity matrix represents the transformation that leaves every vector unchanged.

• CovarianceRelated: Scaling either variable scales covariance by the same factor.

• Affine geometryRelated: The linear part of an affine transformation controls its action on directions.

• Linear operatorRelated: This is the general name for the structure-preserving maps called operators.

• Invariant subspaceRelated: The standard invariant-subspace question concerns linear transformations.

• Invertible matrixRelated: A matrix is invertible precisely when its associated transformation is bijective.

• EigenvectorNarrower topic: Eigenvectors describe the special directions of such a map.

• Orthogonal matrixNarrower topic: An orthogonal matrix represents a linear transformation that preserves the Euclidean inner product.

• Change of variablesCompared with: Linear substitutions have constant Jacobians, unlike general nonlinear changes of variables.

• Kernel (linear algebra)Narrower topic: The kernel is defined for this structure-preserving kind of map.

• Rank (linear algebra)Related: A matrix’s rank is the dimension of the image of its associated linear map.

• Scalar multiplicationRelated: Its defining condition requires preserving scalar multiplication.

• Square matrixRelated: A square matrix represents a linear transformation from a finite-dimensional space to itself.

• Linear functionalNarrower topic: A linear functional is the special case whose output space is the scalar field.

• Bilinear formNarrower topic: Fixing either input of a bilinear form produces a linear map.

• Cayley–Hamilton theoremNarrower topic: A square matrix represents an endomorphism, so the theorem describes an intrinsic property of that map.

• Fréchet derivativeNarrower topic: The first-order approximation must be linear in the input change.

• Matrix inverseRelated: A matrix inverse represents reversing the transformation encoded by a matrix.

• Finite-dimensional vector spaceRelated: Finite bases let linear transformations be represented by matrices.

• Linear functionCompared with: In one dimension it has form f(x) = mx, so a nonzero intercept makes a function affine rather than linear in this strict sense.

• MorphismRelated: Linear maps are morphisms in the category of vector spaces.

• Column spaceNarrower topic: A matrix’s column space is the image of its associated linear transformation.

• Multivariate normal distributionRelated: Applying one to a multivariate normal vector produces another multivariate normal vector.

• Constant functionCompared with: A constant function between vector spaces is linear only in the zero-valued case.

• Differentiable functionRelated: The derivative is the linear map that best describes local change.

• Fundamental theorem of linear algebraNarrower topic: A matrix represents such a map between finite-dimensional vector spaces.

• Binet–Cauchy identityNarrower topic: Matrices in the identity represent composable linear maps between spaces of possibly different dimensions.

• Eigenvalues and eigenvectorsNarrower topic: Eigenvectors describe special directions preserved by this kind of map.

• Linear dynamical systemNarrower topic: The system’s equations use linear maps to relate states, inputs, and outputs.

• Perron–Frobenius theoremNarrower topic: A matrix represents such a map, whose eigenstructure the theorem constrains.

• Algebra over a fieldNarrower topic: Fixing either multiplication input turns the other input into a linear map.

• Woodbury matrix identityNarrower topic: The identity describes how an invertible linear map changes under a low-rank perturbation.

• Dieudonné's theoremCompared with: It induces a collineation only when no nontrivial field automorphism is needed.

• Dimension theorem for vector spacesNarrower topic: The theorem applies to this structure-preserving function.

• Jacobian matrix and determinantRelated: The derivative encoded by a Jacobian is a linear transformation.