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NullSpace

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

MORE INFORMATION

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.

Basic Examples (1)

Find the null space of a 3×3 matrix:

The action of m on the vector is the zero vector:

Generalizations & Extensions (1)

Applications (2)

Properties & Relations (2)

MatrixRank LinearSolve RowReduce SingularValueList Eigenvalues Det Inverse FindLinearRecurrence

Solving Linear Systems

Implementation notes: Numerical and Related Functions

Implementation notes: Algebra and Calculus

NKS|Online (A New Kind of Science)

Linear Systems

Matrices and Linear Algebra

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