specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function)...

related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector...

composition of two linear mappings between finite dimensional vector spaces. Let the linear mapping f map V to W, and let the linear mapping g map W to U....

In plane geometry, a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount proportional to its signed...

In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of...

In linear algebra, a squeeze mapping, also called a squeeze transformation, is a type of linear map that preserves Euclidean area of regions in the Cartesian...

topographic mapping (GTM) use a point representation in the embedded space to form a latent variable model based on a non-linear mapping from the embedded...

complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and...

global tone mapping methods are contrast reduction and color inversion. local (or spatially varying) operators: the parameters of the non-linear function...

advantage that it can be applied to any linear map without need for a specific matrix. Given the same linear mapping f as above, the rank is n minus the dimension...

between two complex vector spaces is said to be antilinear or conjugate-linear if f ( x + y ) = f ( x ) + f ( y )  (additivity)  f ( s x ) = s ¯ f ( x...

bilinear. In the special case when the quadrilateral is a parallelogram, a linear mapping to the unit square exists and the generalization follows easily. The...

(and sometimes even the author). In linear algebra, it is synonymous with a linear form, which is a linear mapping from a vector space V {\displaystyle...

spaces V and W over a field F, a linear map (also called, in some contexts, linear transformation or linear mapping) is a map T : V → W {\displaystyle...

subspace learning. The main linear technique for dimensionality reduction, principal component analysis, performs a linear mapping of the data to a lower-dimensional...

the same trace. As a consequence one can define the trace of a linear operator mapping a finite-dimensional vector space into itself, since all matrices...

Retrieved 2019-12-06. "Mapping, Mathematical | Encyclopedia.com". www.encyclopedia.com. Retrieved 2019-12-06. Lang, Serge (1971). Linear Algebra (2nd ed.)...

as a quadratic form coming with the vector space, see null vector, a linear mapping given as matrix product or dot product, a seminorm in a Minkowski space...

equating to zero the characteristic polynomial of a matrix or of a linear mapping Method of characteristics, a technique for solving partial differential...

In mathematics, an invariant subspace of a linear mapping T : V → V i.e. from some vector space V to itself, is a subspace W of V that is preserved by...

the identity mapping. A linear differential operator (abbreviated, in this article, as linear operator or, simply, operator) is a linear combination of...

theorem (also called inverse mapping theorem or Banach isomorphism theorem), which states that a bijective bounded linear operator T {\displaystyle T}...

VN; W). When N = 1, a multilinear mapping is just an ordinary linear mapping, and the space of all linear mappings from V to W is denoted L(V; W). The...

mathematics, the term linear is used in two distinct senses for two different properties: linearity of a function (or mapping); linearity of a polynomial....

over a differentiable manifold M. An R-linear mapping of sections P : Γ(E) → Γ(F) is said to be a kth-order linear differential operator if it factors through...

bilinear mapping into a K {\displaystyle \mathbb {K} } -vector space Z 1 , {\displaystyle Z_{1},} then there exists a unique linear mapping f : Z → Z...

spaces. The open mapping theorem states that a continuous surjective linear transformation from one Banach space to another is an open mapping meaning that...

z\in \mathbb {H} } corresponds to the C {\displaystyle \mathbb {C} } -linear mapping ρ z : a + j b ↦ z ⋅ ( a + j b ) . {\displaystyle \rho _{z}:a+jb\mapsto...

In linear algebra, linear transformations can be represented by matrices. If T {\displaystyle T} is a linear transformation mapping R n {\displaystyle...

The cokernel of a linear mapping of vector spaces f : X → Y is the quotient space Y / im(f) of the codomain of f by the image of f. The dimension of the...