geometric algebra

E801055
algebraic system branch of mathematics mathematical framework

Geometric algebra is a mathematical framework that unifies and extends vector and complex number algebra to elegantly describe geometry, transformations, and physical laws in a single coherent language.

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Statements (68)

Predicate Object
instanceOf algebraic system ⓘ
branch of mathematics ⓘ
mathematical framework ⓘ
alsoKnownAs Clifford algebra (in many contexts) NERFINISHED ⓘ
appliedIn computer science ⓘ
control theory ⓘ
engineering ⓘ
robot kinematics ⓘ
theoretical physics ⓘ
basedOn Clifford algebra NERFINISHED ⓘ
coreConcept bivector ⓘ
blade ⓘ
geometric product ⓘ
inner product ⓘ
multivector ⓘ
outer product ⓘ
pseudoscalar ⓘ
rotor ⓘ
spinor (in GA sense) ⓘ
trivector ⓘ
versor ⓘ
dimensionOfAlgebra 2^n for an n-dimensional vector space ⓘ
extends Grassmann algebra NERFINISHED ⓘ
complex numbers ⓘ
exterior algebra ⓘ
quaternions NERFINISHED ⓘ
vector spaces ⓘ
feature ability to encode incidence and metric in one algebra ⓘ
compact representation of rotations ⓘ
coordinate-free formulation of geometry ⓘ
unified treatment of scalars, vectors, and higher-grade elements ⓘ
formalizedBy William Kingdon Clifford NERFINISHED ⓘ
hasVariant Euclidean geometric algebra ⓘ
conformal geometric algebra NERFINISHED ⓘ
projective geometric algebra ⓘ
space-time algebra ⓘ
influencedBy Hermann Grassmann NERFINISHED ⓘ
operation dot product ⓘ
geometric product ⓘ
grade projection ⓘ
reverse ⓘ
wedge product ⓘ
represents Lorentz transformations ⓘ
lines ⓘ
planes ⓘ
points ⓘ
reflections as versors ⓘ
rotations as rotors ⓘ
volumes ⓘ
unifies Euclidean geometry ⓘ
affine geometry ⓘ
complex number algebra ⓘ
linear algebra ⓘ
projective geometry ⓘ
quaternion algebra ⓘ
vector algebra ⓘ
usedFor classical mechanics ⓘ
computer graphics ⓘ
computer vision ⓘ
describing geometry ⓘ
describing physical laws ⓘ
describing reflections ⓘ
describing rigid body motions ⓘ
describing rotations ⓘ
electromagnetism ⓘ
quantum mechanics (in some formulations) ⓘ
relativistic physics ⓘ
robotics ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

foundations of geometric algebra as a unified language for physics → hasCoreConcept → geometric algebra ⓘ
subject surface form: Foundations of geometric algebra as a unified language for physics