RowReduce

RowReduce[m]

gives the row‐reduced form of the matrix m.

Details and Options

  • RowReduce performs a version of Gaussian elimination, adding multiples of rows together so as to produce zero elements when possible. The final matrix is in reduced row echelon form.
  • If m is a non‐degenerate square matrix, RowReduce[m] is IdentityMatrix[Length[m]]. »
  • If m is a sufficiently non‐degenerate rectangular matrix with rows and more than columns, then the first columns of RowReduce[m] will form an identity matrix. »
  • RowReduce 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
  • RowReduce[m,Modulus->n] performs row reduction modulo n. »
  • RowReduce[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  (3)

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Do row reduction on a square matrix:

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Do row reduction on a rectangular matrix:

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Scope  (2)

Options  (2)

Applications  (2)

Properties & Relations  (3)

See Also

LinearSolve  Inverse  NullSpace  HermiteDecomposition  SmithDecomposition  GroebnerBasis

Tutorials

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