In mathematics, given a vector space X with an associated quadratic form q, written (X, q), a null vector or isotropic vector is a non-zero element x...

null vectors, called a null basis. Vector fields are called timelike, spacelike, or null if the associated vectors are timelike, spacelike, or null at...

tangent vector is past-directed. These definitions only apply to causal (chronological or null) curves because only timelike or null tangent vectors can be...

trapped null surface is often used interchangeably. However, when discussing causal horizons, trapped null surfaces are defined as only null vector fields...

pseudo-Riemannian geometry, a null hypersurface is a hypersurface whose normal vector at every point is a null vector (has zero length with respect to...

some scalar and vector quantities constructed from arbitrary timelike or null vectors and the matter tensor. First, a unit timelike vector field X → {\displaystyle...

set" (e.g., null set) to "having a value of zero" (e.g., null vector). In a vector space, the null vector is the neutral element of vector addition; depending...

mathematical physics, a null dust solution (sometimes called a null fluid) is a Lorentzian manifold in which the Einstein tensor is null. Such a spacetime can...

0, so that ei + ej is a null vector. In a pseudo-Euclidean space with k < n, unlike in a Euclidean space, there exist vectors with negative scalar square...

a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of the co-domain; the kernel is...

antenna is rotated until the received signal is minimum; at that point the antenna's null is pointed along the bearing line to the transmitter. Null vector...

rows are used to compute the syndrome vector at the receiving end and if the syndrome vector is the null vector (all zeros) then the received word is...

The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection...

homogeneous linear parametric equations, the span of a collection of vectors, and the null space, column space, and row space of a matrix. Geometrically (especially...

physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude...

coordinate vector field dual to the covector field d v {\displaystyle dv} , is a null vector field. Indeed, geometrically speaking, it is a null geodesic...

by using the complex projective vector to construct a null-vector. If ξ {\displaystyle \xi } is a CP1 projective vector, it can be tensored with its Hermitian...

observables. In the case of the NP formalism, the vector basis chosen is a null tetrad: a set of four null vectors—two real, and a complex-conjugate pair. The...

states that any Lorentzian manifold which admits a covariantly constant null vector field k {\displaystyle k} is called a pp-wave spacetime. That is, the...

. Depending on the bilinear form, the vector space may contain null vectors, non-zero self-orthogonal vectors, in which case perpendicularity is replaced...

pair of real null vectors and { m a , m ¯ a } {\displaystyle \{m^{a},{\bar {m}}^{a}\}} is a pair of complex null vectors. These tetrad vectors respect the...

In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an object with four components, which transform in a specific way under...

the speed of light squared. Systems whose four-momentum is a null vector, a light-like vector within the context of Minkowski space (for example, a single...

non-zero vector v in V is said to be isotropic if q(v) = 0. A quadratic form is isotropic if and only if there exists a non-zero isotropic vector (or null vector)...

{\displaystyle \mathbf {A} } ⁠'s null space and is sometimes called a (right) null vector of ⁠ A . {\displaystyle \mathbf {A} .} ⁠ The vector ⁠ x {\displaystyle \mathbf...

a common plane. The three vectors define a three-dimensional space. The vectors o → {\displaystyle {\vec {o}}} (null vector, whose components are equal...

composition algebras does not share the usual properties of a norm since null vectors are allowed. A composition algebra ( A , ∗ , N ) {\displaystyle (A,{}^{*}...

existence of a non-zero v in A such that N(v) = 0, called a null vector. When x is not a null vector, the multiplicative inverse of x is x ∗ N ( x ) {\textstyle...

called a null-vector; then the parallel transport in question is such that it carries any null-vector at one point into the position of a null-vector at a...

implementation internals. This is known as the nil vector. In languages with a tagged architecture, a possibly null pointer can be replaced with a tagged union...