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 .
(ii) two null vectors
are orthogonal if and only if they are linearly dependent;
Therefore, our calculations do not contain null vectors
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).