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searching for Null vector 32 found (70 total)

alternate case: null vector

Trapped surface (610 words) [view diff] exact match in snippet view article find links to article

discussing causal horizons, trapped null surfaces are defined as only null vector fields giving rise to null surfaces. But marginally trapped surfaces
Four-frequency (277 words) [view diff] exact match in snippet view article find links to article
motion. The four-frequency of a photon is always a future-pointing and null vector. An observer moving with four-velocity V b {\displaystyle V^{b}} will
Brinkmann coordinates (327 words) [view diff] exact match in snippet view article find links to article
vector field dual to the covector field d v {\displaystyle dv} , is a null vector field. Indeed, geometrically speaking, it is a null geodesic congruence
Photon surface (419 words) [view diff] exact match in snippet view article find links to article
spacelike hypersurface S of (M, g) such that, for every point p∈S and every null vector k∈TpS, there exists a null geodesic γ {\displaystyle {\gamma }} :(-ε
Recurrent tensor (679 words) [view diff] exact match in snippet view article find links to article
mathematical research. For example, if X {\displaystyle X} is a recurrent non-null vector field on a pseudo-Riemannian manifold satisfying ∇ X = ω ⊗ X {\displaystyle
Null dust solution (752 words) [view diff] exact match in snippet view article find links to article
G^{ab}=8\pi \Phi \,k^{a}\,k^{b}} where k → {\displaystyle {\vec {k}}} is a null vector field. This definition makes sense purely geometrically, but if we place
Two-dimensional conformal field theory (5,674 words) [view diff] exact match in snippet view article find links to article
) = 0 {\displaystyle L_{-1}V_{1,1}(z)=0} , due to the presence of a null vector in the corresponding degenerate representation. An N {\displaystyle N}
Isotropy (1,245 words) [view diff] exact match in snippet view article find links to article
non-zero vector v such that q(v) = 0; such a v is an isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an
Null (radio) (362 words) [view diff] exact match in snippet view article
Independent Local Radio. Independent Broadcasting Authority. p. 10. Archived from the original on 17 April 2024. Retrieved 18 November 2024. Null vector
Kerr–Schild perturbations (312 words) [view diff] exact match in snippet view article find links to article
where V {\displaystyle V} is a scalar and l a {\displaystyle l_{a}} is a null vector with respect to the background spacetime. It can be shown that any perturbation
Classification of electromagnetic fields (1,119 words) [view diff] exact match in snippet view article find links to article
} The skew-symmetry of F implies that: either the eigenvector r is a null vector (i.e. η(r,r) = 0), or the eigenvalue λ is zero, or both. A 1-dimensional
W-algebra (5,488 words) [view diff] exact match in snippet view article find links to article
module of momentum P {\displaystyle P} has a null vector at level r s {\displaystyle rs} . This null vector is itself a primary state of momentum P − r
Numerical continuation (3,831 words) [view diff] exact match in snippet view article find links to article
coefficient of the null vector in the general solution of the Newton system (particular solution plus an arbitrary multiple of the null vector). This method
Lights Out (game) (1,155 words) [view diff] exact match in snippet view article
found that in order for a configuration to be solvable (deriving the null vector from the original configuration) it must be orthogonal to the two vectors
Singular value decomposition (14,592 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \mathbf {A} } ⁠'s null space and is sometimes called a (right) null vector of ⁠ A . {\displaystyle \mathbf {A} .} ⁠ The vector ⁠ x {\displaystyle
Geometric invariant theory (2,272 words) [view diff] exact match in snippet view article find links to article
example – the null orbit is not open because any neighborhood of the null vector contains points in all other orbits, so in the quotient topology any
Moore–Penrose inverse (7,644 words) [view diff] exact match in snippet view article find links to article
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 its
Electrovacuum solution (1,982 words) [view diff] exact match in snippet view article find links to article
nonzero. This possibility is a tensor analogue of the well known that a null vector always has vanishing length, even if it is not the zero vector. Thus
Linear independence (4,400 words) [view diff] exact match in snippet view article find links to article
three-dimensional space. The vectors o → {\displaystyle {\vec {o}}} (null vector, whose components are equal to zero) and k → {\displaystyle {\vec {k}}}
Vaidya metric (3,476 words) [view diff] no match in snippet view article find links to article
mass, σ μ ( x ) {\displaystyle \sigma _{\mu }(x)} is a "flat metric" null-vector field implicitly defined by Eqn. (20), and u ( x ) {\displaystyle u(x)}
Orthogonal matrix (4,802 words) [view diff] exact match in snippet view article find links to article
1 transpositions. A Householder reflection is constructed from a non-null vector v as Q = I − 2 v v T v T v . {\displaystyle Q=I-2{\frac {{\mathbf {v}
Generalized helicoid (1,317 words) [view diff] exact match in snippet view article find links to article
\\r^{2}\end{pmatrix}}\ .} For t = 0 {\displaystyle t=0} the normal vector is the null vector. Hence the directrix consists of singular points. The directrix separates
Goldberg–Sachs theorem (1,251 words) [view diff] exact match in snippet view article find links to article
orthogonal to l a {\displaystyle l^{a}} . It is spanned by a complex null vector m a {\displaystyle m^{a}} and its complex conjugate m ¯ a {\displaystyle
Virasoro algebra (4,140 words) [view diff] exact match in snippet view article find links to article
irreducible if and only if it has no singular vectors. A singular vector or null vector of a highest weight representation is a state that is both descendant
Basis (universal algebra) (2,000 words) [view diff] exact match in snippet view article
function, it is a present basis. Yet, since this space only contains the null vector and its only endomorphism is the identity, any function b from any set
Special relativity (25,048 words) [view diff] exact match in snippet view article find links to article
spacelike or null (lightlike). Note that a null vector is not the same as a zero vector. A null vector is one for which ⁠ A ⋅ A = 0 {\displaystyle A\cdot
Virasoro conformal block (6,417 words) [view diff] exact match in snippet view article find links to article
|L'|} , and diverges for | L | = N {\displaystyle |L|=N} if there is a null vector at level N {\displaystyle N} . Up to | L | = 1 {\displaystyle |L|=1}
Four-vector (8,365 words) [view diff] exact match in snippet view article find links to article
{\mathbf {n} }}\right)=0} so the four-frequency of a photon is always a null vector. The quantities reciprocal to time t and space r are the angular frequency
Gamma matrices (7,303 words) [view diff] exact match in snippet view article find links to article
can adapt the argument for the second result slightly. We pick a non-null vector   q μ   {\displaystyle \ q_{\mu }\ } which is orthogonal to p μ   . {\displaystyle
Modified Kumaraswamy distribution (1,145 words) [view diff] exact match in snippet view article find links to article
{0}}} , where 0 {\displaystyle {\boldsymbol {0}}} is a two-dimensional null vector. If X ∼ MK ( α , β ) {\displaystyle X\sim {\textrm {MK}}(\alpha ,\beta
Optical metric (4,262 words) [view diff] exact match in snippet view article find links to article
refractive index. This is analogous to Kerr-Schild form, which uses a null vector field in place of timelike. An open question is which spacetimes can
Complex quaternion functions (4,052 words) [view diff] exact match in snippet view article find links to article
Adding 2m π i also gives a solution. The log of a quaternion that is a null vector quaternion N does not exist. The above equation diverges as a → 0 {\displaystyle