geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra...

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

geometric algebra is a specific algebraic structure. The term is also used as a blanket term for the theory of geometric algebras. Geometric algebra may...

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...

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

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

means of algebraic methods of some geometrical shapes, called algebraic sets, and defined as common zeros of multivariate polynomials. Algebraic geometry...

physicist and science educator. He is best known as chief architect of geometric algebra as a unified language for mathematics and physics, and as founder...

derived. More generally, in n-dimensional geometric algebra, pseudovectors are the elements of the algebra with dimension n − 1, written ⋀n−1Rn. The label...

In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to...

In mathematics, a universal geometric algebra is a type of geometric algebra generated by real vector spaces endowed with an indefinite quadratic form...

Multilinear Algebra. Hogben, L, ed. (2007). Handbook of Linear Algebra.[page needed] Arthur, John W. (2011). Understanding Geometric Algebra for Electromagnetic...

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

The term "versor" is generalised in geometric algebra to indicate a member R {\displaystyle R} of the algebra that can be expressed as the product of...

spacetime algebra (STA) is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) to physics. Spacetime algebra provides...

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...

In physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra Cl3,0(R) of the three-dimensional Euclidean space as a...

to any vector space F-algebra Geometric algebra – Algebraic structure designed for geometry Non-associative algebra – Algebra over a field where binary...

number in number theory, and the geometrical concept of contact between two algebraic or analytic varieties in algebraic geometry. A field with a valuation...

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...

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

main technical tool of algebraic geometry, and many results and concepts of commutative algebra are strongly related with geometrical concepts. The study...

what is now termed geometric algebra, a special case of the Clifford algebra named in his honour. The operations of geometric algebra have the effect of...

cross products like this. The product can also be calculated using geometric algebra of a seven-dimensional vector space with a positive-definite quadratic...

1957/1958 on geometric algebras that stand in relation to quantum physics and quantum field theory. He pointed out that those algebras can be described...

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

density, are introduced. In geometric algebra (GA) these are multivectors, which sometimes follow Ricci calculus. In the Algebra of physical space (APS),...

introduce geometric spaces from linear algebra, and geometry is often presented, at the elementary level, as a subfield of linear algebra. Linear algebra is...

Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric properties...

from the geometric algebra, a higher level abstraction, in which the quaternions are an even subalgebra. The principal tool in geometric algebra is the...