specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function)...
43 KB (7,001 words) - 21:10, 13 July 2024
In linear algebra, the transpose of a linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of...
15 KB (2,716 words) - 12:41, 17 October 2023
In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of linear spaces and are often used as...
15 KB (2,586 words) - 09:03, 1 June 2024
related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector...
30 KB (4,788 words) - 07:22, 7 February 2024
Piecewise linear function Linear approximation Linear interpolation Discontinuous linear map Linear least squares "The term linear function means a linear form...
5 KB (651 words) - 22:20, 16 August 2024
+ ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b,} linear maps such as: ( x 1 , … , x n ) ↦ a 1 x 1 + ⋯ + a n x n , {\displaystyle (x_{1}...
64 KB (7,780 words) - 04:31, 11 August 2024
conjugate of s . {\displaystyle s.} Antilinear maps stand in contrast to linear maps, which are additive maps that are homogeneous rather than conjugate homogeneous...
10 KB (1,769 words) - 15:02, 31 August 2024
polynomial. An example of a linear function is the function defined by f ( x ) = ( a x , b x ) {\displaystyle f(x)=(ax,bx)} that maps the real line to a line...
12 KB (1,634 words) - 22:12, 7 June 2024
natural linear map F → V ⊗ V'; in the language of linear maps, it assigns to a scalar c the linear map c⋅idV. Sometimes this is called coevaluation map, and...
36 KB (5,385 words) - 00:34, 24 September 2024
piecewise linear or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments. A piecewise linear function...
10 KB (1,201 words) - 00:57, 25 August 2024
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 the co-domain;...
24 KB (3,711 words) - 08:11, 1 August 2024
of paper. The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of...
6 KB (708 words) - 22:05, 28 July 2024
Bounded operator (redirect from Bounded linear map)
codomain. A linear map has this property if and only if it is identically 0. {\displaystyle 0.} Consequently, in functional analysis, when a linear operator...
15 KB (2,471 words) - 12:14, 16 July 2024
Dual space (redirect from Duality (linear algebra))
is defined as the set of all linear maps φ : V → F {\displaystyle \varphi :V\to F} (linear functionals). Since linear maps are vector space homomorphisms...
45 KB (6,872 words) - 18:21, 24 June 2024
Vector space (redirect from Linear space)
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied...
87 KB (11,487 words) - 13:43, 28 September 2024
lesser of the number of rows and columns, and the rank. The rank of a linear map or operator Φ {\displaystyle \Phi } is defined as the dimension of its...
29 KB (4,390 words) - 03:18, 12 September 2024
Affine transformation (redirect from Affine-linear function)
associated vector spaces over the field k. A map f: X → Z is an affine map if there exists a linear map mf : V → W such that mf (x − y) = f (x) − f (y)...
27 KB (3,596 words) - 23:26, 24 August 2024
analysis, spaces of linear maps between two vector spaces can be endowed with a variety of topologies. Studying space of linear maps and these topologies...
37 KB (6,521 words) - 17:21, 21 August 2024
mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments...
9 KB (1,570 words) - 05:29, 9 August 2024
In mathematics, a linear fractional transformation is, roughly speaking, an invertible transformation of the form z ↦ a z + b c z + d . {\displaystyle...
12 KB (1,701 words) - 22:13, 2 September 2024
Isometry (redirect from Linear isometry)
is linear as a map over the real numbers R {\displaystyle \mathbb {R} } . If X and Y are complex vector spaces then A may fail to be linear as a map over...
18 KB (2,351 words) - 20:34, 29 July 2024
Tensor product (redirect from Tensor product of linear maps)
bilinear maps in the sense that a bilinear map from V × W {\displaystyle V\times W} into another vector space Z factors uniquely through a linear map V ⊗ W...
50 KB (8,651 words) - 19:03, 15 August 2024
Equicontinuity (redirect from Equicontinuous linear maps)
the Banach–Steinhaus theorem) states that a set H {\displaystyle H} of linear maps between Banach spaces is equicontinuous if it is pointwise bounded; that...
25 KB (3,751 words) - 22:02, 7 June 2023
In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars...
34 KB (5,967 words) - 23:34, 15 June 2024
article focuses on matrices related to linear algebra, and, unless otherwise specified, all matrices represent linear maps or may be viewed as such. Square...
106 KB (13,088 words) - 21:05, 21 September 2024
this matrix is viewed as a linear map). More generally, the differential or pushforward refers to the derivative of a map between smooth manifolds and...
26 KB (3,903 words) - 11:58, 11 September 2024
Transpose (redirect from Transpose of a linear transformation)
Together with the preceding property, this implies that the transpose is a linear map from the space of m × n matrices to the space of the n × m matrices. (...
20 KB (2,525 words) - 12:30, 8 May 2024
Complex conjugate of a vector space (redirect from Complex conjugate linear map)
{\displaystyle C^{op}\to D.} A linear map f : V → W {\displaystyle f:V\to W\,} gives rise to a corresponding linear map f ¯ : V ¯ → W ¯ {\displaystyle...
6 KB (860 words) - 16:01, 12 December 2023
In linear algebra, a multilinear map is a function of several variables that is linear separately in each variable. More precisely, a multilinear map is...
9 KB (2,235 words) - 19:18, 15 January 2024
Graded vector space (redirect from Graded linear map)
space. For general index sets I, a linear map between two I-graded vector spaces f : V → W is called a graded linear map if it preserves the grading of homogeneous...
6 KB (884 words) - 14:41, 9 August 2023