The following are important identities in vector algebra. Identities that only involve the magnitude of a vector ‖ A ‖ {\displaystyle \|\mathbf {A} \|} and...

portal Vector calculus identities Vector algebra relations Directional derivative Conservative vector field Solenoidal vector field Laplacian vector field...

related to vectors: Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities...

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 mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

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

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

and elements of the vector space (called vectors). Abstract algebra is the name that is commonly given to the study of algebraic structures. The general...

Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space)...

The concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector spaces. This provides...

constant force. Scalar multiplication Matrix multiplication Vector addition Vector algebra relations This set index article includes a list of related items...

In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the...

mathematics and physics CCR algebras (after canonical commutation relations) and CAR algebras (after canonical anticommutation relations) arise from the quantum...

In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for...

Clifford algebra is generated by gamma matrices, matrices that satisfy a set of canonical anti-commutation relations. The spinors are the column vectors on...

displaying short descriptions of redirect targets Vector algebra relations – Formulas about vectors in three-dimensional Euclidean space Wilson, p. 404...

vector fields is isomorphic to the Lie algebra g {\displaystyle {\mathfrak {g}}} of G. Affine vector field Curvature collineation Homothetic vector field...

of the term "vector" as discussed above. Exterior algebra Clifford algebra Antivector, a generalization of pseudovector in Clifford algebra Orientability...

Virasoro relations, i.e., the image of ω is a conformal vector. Conversely, any conformal vector in a vertex algebra induces a distinguished vertex algebra homomorphism...

"algebra" An "algebra", or to be verbose, an algebra over a field, is a vector space equipped with a bilinear vector product. Some notable algebras in...

enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...

the universal enveloping algebra in general. The exterior algebra is constructed from the exterior product. Given a vector space V, the exterior product...

Thm. 5.1, pp. 79. The Virasoro algebra has a presentation in terms of two generators (e.g. L3 and L−2) and six relations. The generators L n > 0 {\displaystyle...

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase...

constructed as a quotient of a free algebra in terms of generators and relations. One construction starts with an abstract vector space V (of dimension 2n) equipped...

εjkl is used. These commutation relations make the Pauli matrices the generators of a representation of the Lie algebra ( R 3 , × ) ≅ s u ( 2 ) ≅ s o (...

a composition algebra and of a unital Banach algebra. Because the product of any two basis vectors is plus or minus another basis vector, the set {±1,...

Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins...

coordinate description of a vector changes by passing from one coordinate system to another. Tensors are objects in multilinear algebra that can have aspects...

group algebra of (the dual to) a vector space is the symmetric algebra, and the group algebra of the Heisenberg group (of the dual) is the Weyl algebra: one...