Plane-based geometric algebra is an application of Clifford algebra to modelling planes, lines, points, and rigid transformations. Generally this is with...

Grassmann–Cayley algebra. In the late 1990s, plane-based geometric algebra and conformal geometric algebra (CGA) respectively provided a framework for...

teaching them. Hamilton's treatment is more geometric than the modern approach, which emphasizes quaternions' algebraic properties. He founded a school of "quaternionists"...

Conformal geometric algebra (CGA) is the geometric algebra constructed over the resultant space of a map from points in an n-dimensional base space Rp...

generalization of principal component analysis Projective Geometric Algebra or Plane-based Geometric Algebra Pentagestrone acetate, a progestin Polyglandular autoimmune...

and the concurrent developments of algebra marked a new stage for geometry, since geometric figures such as plane curves could now be represented analytically...

Geometric Algebra is a book written by Emil Artin and published by Interscience Publishers, New York, in 1957. It was republished in 1988 in the Wiley...

may be constructed via linear algebra, starting from vector spaces over a finite field; the affine and projective planes so constructed are called Galois...

lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to function...

of symbolic algebra, a geometric constructive algebra was developed by classical Greek and Vedic Indian mathematicians in which algebraic equations were...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

Cartesian plane, called the complex plane. This allows a geometric interpretation of the complex numbers and their operations, and conversely some geometric objects...

affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of...

Geometric algebra is an extension of vector algebra, providing additional algebraic structures on vector spaces, with geometric interpretations. Vector...

combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric...

generalize to higher dimensions, but the alternative approach of geometric algebra, which uses the exterior product, does (see § Generalizations below...

uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are not...

area of study based on the theory proposed by Alexander Grothendieck in the 1980s that describes the way a geometric object of an algebraic variety (such...

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

family, one uses algorithmic or geometric techniques that originate from linear algebra or mathematical analysis. Algebra also studies Diophantine equations...

In algebra, a split-complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit j satisfying j 2 = 1 {\displaystyle...

geometric interpretation of the cross product. In exterior algebra the exterior product of two vectors is a bivector. A bivector is an oriented plane...

rings, algebras and function spaces. The term vector is generally not used for elements of these vector spaces, and is generally reserved for geometric vectors...

expression of problems of geometry in terms of algebra and calculus. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described...

two distinct composition algebras. The preceding sections of this article deal with the complex plane in terms of a geometric representation of the complex...

the Elements states results of what are now called algebra and number theory, explained in geometrical language. For more than two thousand years, the adjective...

attempting to preserve the geometric intuition behind the original definition.: 58  Conventions regarding the definition of an algebraic variety differ slightly...

hand, the plane of the two vectors is represented by the exterior product or wedge product, denoted by a ∧ b. In this context of geometric algebra, this bivector...

This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory...

In algebraic geometry, the geometric genus is a basic birational invariant pg of algebraic varieties and complex manifolds. The geometric genus can be...