NullSpace
NullSpace[m]
gives a list of vectors that forms a basis for the null space of the matrix m.
Details and Options

- NullSpace works on both numerical and symbolic matrices.
- The following options can be given:
-
Method Automatic method to use Modulus 0 integer modulus to use Tolerance Automatic numerical tolerance to use ZeroTest Automatic function to test whether matrix elements should be considered to be zero - NullSpace[m,Modulus->n] finds null spaces for integer matrices modulo n.
- NullSpace[m,ZeroTest->test] evaluates test[m[[i,j]]] to determine whether matrix elements are zero.
- Possible settings for the Method option include "CofactorExpansion", "DivisionFreeRowReduction", and "OneStepRowReduction". The default setting of Automatic switches among these methods depending on the matrix given.
Examples
open allclose allBasic Examples (1)
Scope (10)
Basic Uses (6)
Special Matrices (4)
Null space of a sparse matrix:
Null space of structured matrices:
IdentityMatrix[n] always has an empty null space::
The null space of IdentityMatrix[{m,n}] is non-empty:
Compute the null space for HilbertMatrix:
Options (1)
Applications (2)
Properties & Relations (2)
Arbitrary linear combinations of the null space of m give zero:
m is a 3×4 matrix of random zeros and ones:
The MatrixRank equals the column dimension of m minus the dimension of the null space:
Text
Wolfram Research (1988), NullSpace, Wolfram Language function, https://reference.wolfram.com/language/ref/NullSpace.html (updated 1996).
BibTeX
BibLaTeX
CMS
Wolfram Language. 1988. "NullSpace." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/NullSpace.html.
APA
Wolfram Language. (1988). NullSpace. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NullSpace.html