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# Null Vector

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).

5. When applied to a vector, a null vector is a nonzero vector such that for a given vector , the dot product satisfies . (This use may be slightly nonstandard, but appears for example in the Wolfram Language's FindIntegerNullVector function.)

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## References

Jeffreys, H. and Jeffreys, B. S. "Direction Vectors." §2.033 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, p. 64, 1988.Sommer, G. Geometric Computing with Clifford Algebras. Springer, 2001.

Null Vector

## Cite this as:

Weisstein, Eric W. "Null Vector." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NullVector.html