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...

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...

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...

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...

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...

algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are...

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...

Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems...

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...

and originator of Map Algebra, a vocabulary and conceptual framework for classifying ways to combine map data to produce new maps. Tomlin's teaching...

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...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

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,...

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...

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...

Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins...

mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties...

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...

In mathematics, a ring is an algebraic structure consisting of a set with two binary operations called addition and multiplication, which obey the same...

A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative...

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)...

"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...

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...

In algebraic geometry, a finite morphism between two affine varieties X , Y {\displaystyle X,Y} is a dense regular map which induces isomorphic inclusion...

representing commutative Banach algebras as algebras of continuous functions; the fact that for commutative C*-algebras, this representation is an isometric...

In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have x...

infinite-dimensional Lie algebra called a current algebra. Mathematically these are Lie algebras consisting of smooth maps from a manifold into a finite...

elevation, which allows software to perform map algebra functions to build precise topography maps. These topographic maps can be used to correlate crop health...