Knowra Geometric algebra Geometric algebra Geometric algebra is an algebra of vectors and multivectors that encodes geometric relations through the geometric product, combining inner and outer products in one operation.
Geometric product : A vector product whose symmetric part is the inner product and whose antisymmetric part is the outer product. This defining operation combines lengths, angles, and oriented area.
Vector space : A set of vectors with operations of addition and scalar multiplication satisfying linearity axioms. The algebra begins with vectors and extends their product structure.
Conformal geometric algebra : A geometric algebra model that represents Euclidean points, spheres, and related transformations in a higher-dimensional space. It turns many geometric objects and transformations into algebraic operations.
Vector calculus : The calculus of scalar and vector fields using operations such as gradient, divergence, and curl. Geometric algebra can combine several vector-calculus operations into multivector equations.
William Kingdon Clifford : A nineteenth-century English mathematician who introduced the algebras now named after him. His algebraic construction supplies the mathematical foundation for geometric algebra.
Multivector : An algebraic sum of elements of different grades, such as scalars, vectors, bivectors, and higher-grade elements. Geometric algebra calculations use multivectors to represent mixed geometric quantities.
Inner product space : A vector space equipped with a bilinear inner product that defines lengths and angles. Its metric information determines how vectors multiply geometrically.
Geometric algebra in computer graphics : The use of multivectors and versors to represent and compute geometric transformations in computer graphics. Rotors and reflections provide alternatives to matrix-based transformation pipelines.
Tensor algebra : An algebraic framework for multilinear quantities and their transformations across vector spaces. Tensor methods generalize broadly, while geometric algebra makes metric and oriented-subspace products explicit.
Clifford algebra : An associative algebra generated by a vector space with a quadratic form imposing relations on products of vectors. The modern subject developed by interpreting this algebra geometrically.
Show all 25