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.


open allclose all

Basic Examples  (1)

Find the number of linearly independent rows:

Click for copyable input

Scope  (5)

Options  (2)

Applications  (2)

Properties & Relations  (4)

Possible Issues  (1)

See Also

NullSpace  Det  Eigensystem  RowReduce  SingularValueList  Inverse


Introduced in 2003
| Updated in 2007