KnowraLinear mapLinked fromLinked fromThe 51 pages that link to Linear map, each with the reason it gives.All 51Related 22Narrower topic 25Compared with 4EigenvalueNarrower topic: Eigenvalues describe how a linear transformation acts along special vector directions.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.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.Rotation matrixNarrower topic: A rotation matrix is a coordinate representation of a linear transformation.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.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.Kernel (linear algebra)Narrower topic: The kernel is defined for this structure-preserving kind of map.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.Column spaceNarrower topic: A matrix’s column space is the image of its associated linear transformation.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.Dimension theorem for vector spacesNarrower topic: The theorem applies to this structure-preserving function.Rouché–Capelli theoremNarrower topic: A system is solvable precisely when its constants vector lies in the transformation’s image.
KnowraLinear mapLinked fromLinked fromThe 51 pages that link to Linear map, each with the reason it gives.All 51Related 22Narrower topic 25Compared with 4EigenvalueNarrower topic: Eigenvalues describe how a linear transformation acts along special vector directions.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.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.Rotation matrixNarrower topic: A rotation matrix is a coordinate representation of a linear transformation.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.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.Kernel (linear algebra)Narrower topic: The kernel is defined for this structure-preserving kind of map.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.Column spaceNarrower topic: A matrix’s column space is the image of its associated linear transformation.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.Dimension theorem for vector spacesNarrower topic: The theorem applies to this structure-preserving function.Rouché–Capelli theoremNarrower topic: A system is solvable precisely when its constants vector lies in the transformation’s image.