null vector


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null vector

[′nəl ′vek·tər]
(mathematics)
A vector whose invariant length, that is, the sum over the coordinates of the vector space of the product of its covariant component and contravariant component, is equal to zero.
(relativity)
In special relativity, a four vector whose spatial part in any Lorentz frame has a magnitude equal to the speed of light multiplied by its time part in that frame; a special case of the mathematics definition.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In this short communication we study supergravity solutions preserving a nonminimal fraction of supersymmetries by determining the existence of additional non-space-like isometries in the class of higher-dimensional Kundt space-time admitting a covariantly constant null vector field (CCNV) [6, 7].
It follows that dim [P.sub.2] [less than or equal to] dim [P.sup.[omega].sub.1] = 1, so the curve [[??].sub.2] is a straight line, which may be parametrized as follows: [[??].sub.2]([upsilon]) = [e.sub.0][upsilon], where [e.sub.0] is a null vector of [D.sup.2].
Therefore, the complex vector P is a complex null vector which represents the lightlike nature of the photon.
The set of all integral curves given by a unit nonnull or null vector field u is called the congruence of nonnull or null curves.
Nulling: where we use the null vector wki to null out the undesired signals and obtain the required one.
Since A(x - y) must be in R(A) and p is not, both sides vanish, implying that x - y is a null vector of A and q* y must be zero.
If g(D(s),D(s)) = 0 for all s [member of] [0, L], then u(s) = 0 and the direction D(s) is a null vector given by
(iii) timelike vector is never orthogonal to a null vector.
A regular curve [alpha] : I [right arrow] [R.sup.3.sub.1], I [subset] R in [R.sup.3.sub.1] is said to be spacelike, timelike and null curve if the velocity vector [alpha][phi](t) is a spacelike, timelike and null vector, respectively [3].
(PN1) [v.sub.p] = [[epsilon].sub.0] iff (if and only if) p = [theta], here [theta] is the null vector of V;
Then [[xi].sub.3] is the vector field [C.sup.[perpendicular]] and [[xi].sub.4] is the unique null vector field perpendicular to the plane {[[xi].sub.1], [[xi].sub.2]}, such that {[[xi].sub.3], [[xi].sub.4]) = 1.
where [lambda] is a complex constant and y is a constant vector (an element of the space [C.sup.N]) which depends upon [lambda] and which we desire to be nontrivial, that is, not equal to 0, the null vector. Substituting (1.10) into (1.8), we obtain