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searching for Null vector 32 found (70 total)

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) (270 words) [view diff] exact match in snippet view article

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

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 (14,584 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

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

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

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}}}

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

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}

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

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

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 (25,022 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 (7,254 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

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

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

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