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...

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...

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

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...

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....

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...

(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...

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...

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...

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, 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...

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

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...

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

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

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...

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...

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...

\\p_{m}(a_{n-1})\end{bmatrix}}} This function C {\displaystyle C} is a linear mapping, that is, it satisfies C ( m ) = A m {\displaystyle C(m)=Am} for the...

terms of multilinear mappings. Amongst the advantages of this approach are that it gives a way to show that many linear mappings are "natural" or "geometric"...

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

\operatorname {ad} (x)} .) Since a bracket is bilinear, this determines the linear mapping ad : g → g l ( g ) = ( End ⁡ ( g ) , [ , ] ) {\displaystyle \operatorname...

{\displaystyle V=\mathbb {R} ^{n}} and A : V → V {\displaystyle A:V\to V} be a linear mapping. Then, the weak formulation of the equation A u = f {\displaystyle Au=f}...

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...

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...