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...

+,+,+,\cdots )} metric signature. We say that a tangent vector is non-spacelike if it is null or timelike. The canonical Lorentzian manifold is Minkowski...

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...

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...

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...

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...

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...

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

Switched-mode power supply 0 vector, or null vector, a vector where all components are zero 0 vector space; see Examples of vector spaces 0-velocity surface...

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

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

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...

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...

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

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...

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...

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...

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...

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...

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...

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...

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

scientific research, the null hypothesis (often denoted H0) is the claim that the effect being studied does not exist. The null hypothesis can also be described...

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...

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

are determined so to best approximate, in a least squares sense, the null vector. The newly determined coefficients are then used to extrapolate the function...

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...