There are several meanings of "null vector" in mathematics.

1. The most common meaning of null vector is the -dimensional vector of length 0. i.e., the vector with components, each of which is 0 (Jeffreys and Jeffreys 1988,
p. 64).

2. When applied to a matrix , a null vector is a nonzero vector with the property that .

3. When applied to a vector space with an associated quadratic form , a null vector is a nonzero element of
for which .

4. When applied to a geometric product satisfying the contraction rule for an element of an -vector space, a null vector is a value of such that but (Sommer 2001, pp. 5-6).