Null vector

A pseudo-Euclidean vector space may be decomposed (non-uniquely) into orthogonal subspaces A and B, X = A + B, where q is positive-definite on A and negative-definite on B.

The null cone is also the union of the isotropic lines through the origin.

In particular, these algebras have two imaginary units, which commute so their product, when squared, yields +1: The real subalgebras, split complex numbers, split quaternions, and split-octonions, with their null cones representing the light tracking into and out of 0 ∈ A, suggest spacetime topology.

Null vectors are also used in the Newman–Penrose formalism approach to spacetime manifolds.

[3] In the Verma module of a Lie algebra there are null vectors.