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:
  • MethodAutomaticmethod to use
    Modulus0integer modulus to use
    ToleranceAutomaticnumerical tolerance to use
    ZeroTestAutomaticfunction 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

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Basic Examples  (1)

Find the null space of a 3×3 matrix:

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

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Scope  (2)

Generalizations & Extensions  (1)

Options  (1)

Applications  (2)

Properties & Relations  (2)

See Also

MatrixRank  LinearSolve  RowReduce  SingularValueList  Eigenvalues  Det  Inverse  FindLinearRecurrence

Tutorials

Introduced in 1988
(1.0)
| Updated in 1996
(3.0)