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.
References in periodicals archive ?
The other approach uses null vectors [l.sub.a] (i.e., [l.sup.2] = 0) and leads to the following scalar equation:
We can observe that this matrix is not square as expected; however, it has null vectors:
Let ([bar.M], [bar.g]) be null geodesically complete spacetime obeying the null energy condition [bar.Ric](X, X) [greater than or equal to] 0 for all null vectors X such that the hypothesis of Theorem 1 holds.
In practice, just one refinement step is necessary to fully tighten the null vectors.
Vectors i and 64 are null vectors, which generate zero voltage in the output.
In Minkowski 3-space, a spacelike curve whose principal normal N and binormal B are null vectors is called pseudo null curve [2].
(ii) two null vectors are orthogonal if and only if they are linearly dependent;
As g(x(0), [u.sub.y]) = 1, the plane P in [T.sub.y]M, spanned by the null vectors x(0) and [u.sub.y] (cf.
* An intermediate loop in i, running from b to b + d + 1 at most, in which [A.sub.ii] is determined and in which the null vectors of [H.sub.b] of degree i - 1 are calculated.
To be specific, let us introduce a complete orthogonal set of null vectors [n.sub.(x)] = (1,1,0,0), [n.sub.(y)] = (1,0,1,0), and [n.sub.(z)] = (1,0, 0,1), as well as a set of orthonormal spacelike vectors [d.sub.(x)] = (0,1,0,0), [d.sub.(y)] = (0, 0,1,0), and [d.sub.(z)] = (0,0, 0,1).
Otherwise, a possible set of eigenvectors (w, [W.sup.-1] Aw) is defined by n - m vectors w that are linearly independent null vectors of a, and s additional null vectors of YA that are not null vectors of A, that is, w satisfies 0 [not equal to] aw [member of] null(Y).