Map algebra is an algebra for manipulating geographic data, primarily fields. Developed by Dr. Dana Tomlin and others in the late 1970s, it is a set of...
15 KB (1,923 words) - 09:05, 15 October 2023
Linear algebra is the branch of mathematics concerning linear equations such as: a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...
64 KB (7,780 words) - 04:31, 11 August 2024
also called a regular map. A morphism from an algebraic variety to the affine line is also called a regular function. A regular map whose inverse is also...
26 KB (4,319 words) - 05:17, 25 August 2024
In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center...
30 KB (4,256 words) - 10:18, 18 August 2024
In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...
61 KB (10,457 words) - 02:56, 14 July 2024
"linear transformation" in linear algebra, etc. Some authors, such as Serge Lang, use "function" only to refer to maps in which the codomain is a set of...
6 KB (708 words) - 22:05, 28 July 2024
mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...
11 KB (1,359 words) - 23:57, 25 May 2024
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...
76 KB (12,096 words) - 15:19, 19 August 2024
Heyting algebra Hopf algebra Non-associative algebra Outline of algebra Relational algebra Sigma-algebra Symmetric algebra T-algebra Tensor algebra When...
135 KB (13,099 words) - 07:39, 20 August 2024
Dana Tomlin (section Map algebra)
and originator of Map Algebra, a vocabulary and conceptual framework for classifying ways to combine map data to produce new maps. Tomlin's teaching...
6 KB (638 words) - 21:44, 12 June 2024
linear map f from V to a commutative algebra A, there is a unique algebra homomorphism g : S(V) → A such that f = g ∘ i, where i is the inclusion map of V...
13 KB (2,034 words) - 13:17, 31 January 2024
representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms...
28 KB (4,308 words) - 17:20, 8 November 2023
mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...
64 KB (9,171 words) - 11:01, 7 August 2024
Dual space (redirect from Duality (linear algebra))
the space of linear maps is actually an algebra under composition of maps, and the assignment is then an antihomomorphism of algebras, meaning that (fg)∗...
45 KB (6,872 words) - 18:21, 24 June 2024
In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation...
18 KB (2,553 words) - 09:07, 5 May 2024
In the theory of Lie groups, the exponential map is a map from the Lie algebra g {\displaystyle {\mathfrak {g}}} of a Lie group G {\displaystyle G} to...
13 KB (2,207 words) - 21:53, 8 July 2024
mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties...
20 KB (2,829 words) - 11:21, 17 April 2024
In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the...
23 KB (4,160 words) - 15:09, 12 January 2024
mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure...
22 KB (2,935 words) - 02:08, 13 August 2024
created the web application ColorBrewer. Dana Tomlin – originator of map algebra Doreen Massey (1944–2016) – scholar in the space and places of globalization...
93 KB (9,531 words) - 06:34, 12 August 2024
derivation is a function on an algebra that generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field...
7 KB (1,064 words) - 08:24, 25 May 2024
Finite morphism (redirect from Finite map (algebraic geometry))
In algebraic geometry, a finite morphism between two affine varieties X , Y {\displaystyle X,Y} is a dense regular map which induces isomorphic inclusion...
6 KB (860 words) - 01:49, 25 May 2024
Chain complex (redirect from Complex (in homological algebra))
called its cohomology. In algebraic topology, the singular chain complex of a topological space X is constructed using continuous maps from a simplex to X,...
13 KB (2,029 words) - 20:38, 17 December 2023
Cartography (redirect from Map making)
chartēs, 'papyrus, sheet of paper, map'; and γράφειν graphein, 'write') is the study and practice of making and using maps. Combining science, aesthetics...
61 KB (7,317 words) - 15:55, 2 August 2024
phenomenology. Formally, a Hopf algebra is an (associative and coassociative) bialgebra H over a field K together with a K-linear map S: H → H (called the antipode)...
35 KB (4,397 words) - 17:50, 19 August 2024
In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field) on a set X is a nonempty collection Σ of subsets of X...
30 KB (5,341 words) - 11:48, 23 August 2024
Ring (mathematics) (redirect from Ring (algebra))
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist...
99 KB (13,632 words) - 08:46, 14 August 2024
mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A {\displaystyle A} over the real or complex...
17 KB (2,602 words) - 13:01, 17 July 2024
Linear function (section As a linear map)
function is often used. In linear algebra, mathematical analysis, and functional analysis, a linear function is a linear map. In calculus, analytic geometry...
5 KB (651 words) - 22:20, 16 August 2024
GeoSpace. Retrieved 2 May 2022. Ward, Alan (30 March 2004). "Gravity Anomaly Maps and the Geoid". NASA Earth Observatory. Retrieved 15 January 2024. Ghosh...
4 KB (503 words) - 21:04, 24 July 2024