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...

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...

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

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...

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...

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...

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...

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...

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...

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

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...

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...

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...

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...

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...

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...

mass times the speed of light squared. Systems whose four-momentum is a null vector (for example, a single photon or many photons moving in exactly the same...

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

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,{}^{*}...

the Euclidean distance between the vectors which were normalized to unit sum of squared values within them. Null distribution: For data which can be...

state as well. (Whether the null vector counts as a valid state ("no system present") is a matter of definition. The null vector does not at any rate describe...

pseudoinverse of the null (all zero) vector is the transposed null vector. The pseudoinverse of a non-null vector is the conjugate transposed vector divided by...

the vectors are referred to as timelike, spacelike or null (lightlike). Note that a null vector is not the same as a zero vector. A null vector is one...

subspace Null space, nullity Rank–nullity theorem Nullity theorem Dual space Linear function Linear functional Category of vector spaces Topological vector space...

In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction...