gives the rank of the matrix m.

Details and Options

  • MatrixRank works on both numerical and symbolic matrices.
  • The rank of a matrix is the number of linearly independent rows or columns.
  • MatrixRank[m,Modulus->n] finds the rank for integer matrices modulo n.
  • MatrixRank[m,ZeroTest->test] evaluates test[m[[i,j]]] to determine whether matrix elements are zero. The default setting is ZeroTest->Automatic.
  • MatrixRank[m,Tolerance->t] gives the minimum rank with each element in a numerical matrix assumed to be correct only to within tolerance t.
  • MatrixRank works with sparse arrays.


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Basic Examples  (1)

Find the number of linearly independent rows:

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Scope  (5)

Options  (2)

Applications  (2)

Properties & Relations  (4)

Possible Issues  (1)

Introduced in 2003
Updated in 2007