Where g ^ { \ mu \ nu } are the components of the metric tensor and l ^ \ mu and n ^ \ nu are the components of the principal null vectors:
22.
In Minkowski spacetime, the nonholonomically constructed null vectors \ { l ^ a \,, n ^ a \ } respectively match the outgoing and ingoing " null radial " rays.
23.
From the form of the general coordinate basis expression given above, it is apparent that the stress energy tensor has precisely the same isotropy group as the null vector field \ vec { k }.
24.
As long as nothing happens during transmission, "'r "'will remain in the kernel of "'H "'and the multiplication will yield the null vector.
25.
Systems whose four-momentum is a null vector ( for example a single photon or many photons moving in exactly the same direction ) have zero invariant mass, and are referred to as " massless ".
26.
In several cases " N " is an isotropic quadratic form so that " A " has at least one null vector, contrary to the separation of points required for the usual norm discussed in this article.
27.
Yet, since this space only contains the null vector and its only endomorphism is the identity, any function " b " from any set I ( even a nonempty one ) to this singleton space work as a present basis.
28.
Similarly, Hamming codes cannot detect or recover from an arbitrary three-bit error; Consider the diagram : if the bit in the green circle ( colored red ) were 1, the parity checking would return the null vector, indicating that there is no error in the codeword.
29.
These each may split into three cases according to whether is positive, zero or negative, corresponding ( in reversed order in some cases ) to the object as listed, a degenerate case of a single point, or no points ( where the nonzero solutions of exclude null vectors ).
30.
These rows are used to compute the "'syndrome vector "'at the receiving end and if the syndrome vector is the null vector ( all zeros ) then the received word is error-free; if non-zero then the value indicates which bit has been flipped.
