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:
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
- 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.
Examplesopen allclose all
This is the equivalent to what is given by Inverse:
Properties & Relations (3)
The last three columns of the result are Inverse[m]:
m has its maximal MatrixRank of 3:
The first 3 columns of RowReduce[m] are the 3×3 identity matrix:
Wolfram Research (1988), RowReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/RowReduce.html (updated 1996).
Wolfram Language. 1988. "RowReduce." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/RowReduce.html.
Wolfram Language. (1988). RowReduce. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RowReduce.html