# Category: Geometric algebra

Plane of rotation
In geometry, a plane of rotation is an abstract object used to describe or visualize rotations in space. In three dimensions it is an alternative to the axis of rotation, but unlike the axis of rotati
Comparison of vector algebra and geometric algebra
Geometric algebra is an extension of vector algebra, providing additional algebraic structures on vector spaces, with geometric interpretations. Vector algebra uses all dimensions and signatures, as d
Gauge theory gravity
Gauge theory gravity (GTG) is a theory of gravitation cast in the mathematical language of geometric algebra. To those familiar with general relativity, it is highly reminiscent of the tetrad formalis
In the study of geometric algebras, a k-blade or a simple k-vector is a generalization of the concept of scalars and vectors to include simple bivectors, trivectors, etc. Specifically, a k-blade is a
Plücker coordinates
In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, P3. Because they satisfy a quadr
Bivector
In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. If a scalar is considered a degree-zero quantity, and a vect
Geometric calculus
In mathematics, geometric calculus extends the geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to encompass other mathematical theories includi
Quadric geometric algebra (QGA) is a geometrical application of the geometric algebra. This algebra is also known as the Clifford algebra. QGA is a super-algebra over conformal geometric algebra (CGA)
Spacetime algebra
In mathematical physics, spacetime algebra (STA) is a name for the Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4). According to David Hestenes, spacetime algebra can be particu
Pseudoscalar
In linear algebra, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion while a true scalar does not. Any scalar product between a pseudovector
Paravector
The name paravector is used for the sum of a scalar and a vector in any Clifford algebra, known as geometric algebra among physicists. This name was given by J. G. Maks in a doctoral dissertation at T
Formal moduli
In mathematics, formal moduli are an aspect of the theory of moduli spaces (of algebraic varieties or vector bundles, for example), closely linked to deformation theory and formal geometry. Roughly sp
Universal geometric algebra
In mathematics, a universal geometric algebra is a type of geometric algebra generated by real vector spaces endowed with an indefinite quadratic form. Some authors restrict this to the infinite-dimen
Riemann–Silberstein vector
In mathematical physics, in particular electromagnetism, the Riemann–Silberstein vector or Weber vector named after Bernhard Riemann, Heinrich Martin Weber and Ludwik Silberstein, (or sometimes ambigu
René Descartes
René Descartes (/deɪˈkɑːrt/ or UK: /ˈdeɪkɑːrt/; French: [ʁəne dekaʁt]; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely co
Multivector
In multilinear algebra, a multivector, sometimes called Clifford number, is an element of the exterior algebra Λ(V) of a vector space V. This algebra is graded, associative and alternating, and consis
Outermorphism
In geometric algebra, the outermorphism of a linear function between vector spaces is a natural extension of the map to arbitrary multivectors. It is the unique unital algebra homomorphism of exterior
Geometric algebra
In mathematics, a geometric algebra (also known as a real Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors. Geometric algebra is built out of tw
Conformal geometric algebra
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,q to null vectors in Rp+1,q+1. This allows operat
Algebra of physical space
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 model for (3+1)-dimensional spacetime, representi
Rotor (mathematics)
A rotor is an object in the geometric algebra (also called Clifford algebra) of a vector space that represents a rotation about the origin. The term originated with William Kingdon Clifford, in showin
Semi-orthogonal matrix
In linear algebra, a semi-orthogonal matrix is a non-square matrix with real entries where: if the number of columns exceeds the number of rows, then the rows are orthonormal vectors; but if the numbe