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Inverse

  • Inverse[ m ] gives the inverse of a square matrix m.
  • Inverse works on both symbolic and numerical matrices.
  • For matrices with approximate real or complex numbers, the inverse is generated to the maximum possible precision given the input. A warning is given for ill-conditioned matrices.
  • Inverse[ m , Modulus-> n ] evaluates the inverse modulo n.
  • Inverse[ m , ZeroTest -> test ] evaluates test [ m [[ i , j ]] ] to determine whether matrix elements are zero. The default setting is ZeroTest -> (# == 0 &).
  • A Method option can also be given. Possible settings are as for LinearSolve.
  • See the Mathematica book: Section 1.8.3Section 3.7.6.
  • See also Implementation NotesA.9.44.27MainBookLinkOldButtonDataA.9.44.27Implementation NotesA.9.44.29MainBookLinkOldButtonDataA.9.44.29.
  • See also: PseudoInverse, LinearSolve, RowReduce, NullSpace.
  • Related package: LinearAlgebra`Tridiagonal`.

    Further Examples

    The inverse of a 2 x 2 matrix displayed as a matrix.

    In[1]:=

    Out[1]//MatrixForm=

    If the matrix is singular, the inverse is not computed.

    In[2]:=

    Inverse::sing: Matrix {{1, 3}, {2, 6}} is singular.

    Out[2]=

    If the matrix is not square, the inverse is not computed.

    In[3]:=

    Inverse::matsq: Argument {{1, 2, 2}, {3, 1, 4}} at position 1 is not a square matrix.

    Out[3]=

    You can compute inverse of inexact matrices.

    In[4]:=

    Out[4]//MatrixForm=

    Here is the inverse over the integers modulo 5.

    In[5]:=

    Out[5]//MatrixForm=

    This checks the result.

    In[6]:=

    Out[6]//MatrixForm=