TOPICS
Null Space
If
is alinear transformation of
, then the null space Null(
), also called thekernel
, is the set of allvectors
such that
 |
i.e.,
 |
The term "null space" is most commonly written as two separate words (e.g., Golub and Van Loan 1989, pp. 49 and 602; Zwillinger 1995, p. 128), although other authors write it as a single word "nullspace" (e.g., Anton 1994, p. 259; Robbin 1995, pp. 123 and 180).
Each null space vector corresponds to a zeroeigenvector of the transformation matrix of
.
TheWolfram Language commandNullSpace[
v1,v2, ...
] returns a list of vectors forming avector basis for the nullspace of a set of vectors
over the rationals (or more generally, over whatever base field contains the input vectors).
See also
Fredholm's Theorem,Kernel,Linear Transformation,Nullity,Rank-Nullity Theorem,Vector Basis,Vector Space SpanExplore with Wolfram|Alpha
More things to try:
References
Anton, H.Calculus: A New Horizon, 6th ed. New York: Wiley, 1999.Golub, G. H. and Van Loan, C. F.Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.Robbin, J. W.Matrix Algebra Using MINImal MATlab. Wellesley, MA: A K Peters, 1995.Zwillinger, D. (Ed.).CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, 1995.Referenced on Wolfram|Alpha
Null SpaceCite this as:
Weisstein, Eric W. "Null Space." FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/NullSpace.html