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"...

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

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

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...

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...

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

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...

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

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

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

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...

component of the identity of the orthogonal group). Geometric algebra is a name for the Clifford algebra in an applied setting. The Pauli matrices correspond...

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...

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

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

sub-groups of other transformation groups. Many geometric transformations are expressed with linear algebra. The bijective linear transformations are elements...

the algebra by formulating the problem for the unit circle and two given points a {\displaystyle a} and b {\displaystyle b} in the complex plane. With...

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

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

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...

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

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

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

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

z + b . {\displaystyle z\mapsto az+b.} In the geometric algebra of the Euclidean plane, the geometric product or quotient of two arbitrary vectors is...