In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space...

operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces...

In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional...

physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under continuous rigid transformations such as rotations...

lists, arrays, bit vectors, and strings. The name is derived from the fact that these expressions are interpreted within ("modulo") a certain formal theory...

of equidistribution modulo 1: The sequence vn of vectors in Rk is equidistributed modulo 1 if and only if for any non-zero vector ℓ ∈ Zk, lim n → ∞ 1...

{R} ^{2}} . A similar process can be used to form the direct sum of two vector spaces or two modules. Direct sums can also be formed with any finite number...

value modulo an integer multiple of 2π. In particular, a reflex angle π < θ < 2π equals the negative angle −π < θ − 2π < 0. The angle of two vectors does...

-dimensional integer vector. In order to perform the inverse transform, divide by k {\displaystyle k} ; that is, k is also a unit modulo n . {\displaystyle...

In linear algebra, the quotient of a vector space V {\displaystyle V} by a subspace N {\displaystyle N} is a vector space obtained by "collapsing" N {\displaystyle...

typefaces to group symbols by type (for example, boldface is often used for vectors and uppercase for matrices). The use of specific Latin and Greek letters...

In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative)...

space of the graph (taken modulo 2) has a cycle basis in which each edge of the graph participates in at most two basis vectors. For any cycle c in a graph...

general, may not be reduced modulo 2). It is then possible to reduce all coefficients modulo 2, which will give a modular form modulo 2. Modular forms are generated...

substructures of a larger one. For example, all subspaces of dimension one of a vector space are isomorphic and cannot be identified. An automorphism is an isomorphism...

and a unit vector for the axis, or as a Euclidean vector obtained by multiplying the angle with this unit vector, called the rotation vector (although...

{\displaystyle N_{1}(X)} be the real vector space of 1-cycles (real linear combinations of curves in X) modulo numerical equivalence, meaning that two...

lightlike 4-vector is orthogonal to itself. Invariance of the magnitude of a vector: The magnitude of a vector is the inner product of a 4-vector with itself...

(homothecy), the linear maps from E to E that map orthogonal vectors to orthogonal vectors. The orthogonal O(n) is the subgroup of the general linear group...

the relative velocity vector onto the LOS direction. Equivalently, radial speed equals the norm of the radial velocity, modulo the sign. In astronomy...

and it follows that φ {\displaystyle \varphi } is only defined modulo π. The vector equation of the line through points A and B is given by r = O A +...

In 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...

In mathematics, the discussion of vector fields on spheres was a classical problem of differential topology, beginning with the hairy ball theorem, and...

Witt vector is an infinite sequence of elements of a commutative ring. Ernst Witt showed how to put a ring structure on the set of Witt vectors, in such...

invariants of a real vector bundle that describe the obstructions to constructing everywhere independent sets of sections of the vector bundle. Stiefel–Whitney...

differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a...

algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient Greek language: ὁμός...

vector space. The case of the Real line is the easiest to explain. This type of differential is also known as a covariant vector or cotangent vector,...

operation fails to be commutative Iverson bracket, notation Lie bracket of vector fields, operator Dirac notation, in quantum mechanics Moment, measures relating...

conditional operator Null coalescing operators Safe navigation operators Modulo operators Evaluation strategy List of "Hello World" programs Comparison...