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NullSpace

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

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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.

The possible settings for the Method option are as for LinearSolve.

Basic Examples (1)

Find the null space of a 3x3 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

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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