Wolfram Language & System 11.0 (2016)|Legacy Documentation

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finds the pseudoinverse of a rectangular matrix.

Details and OptionsDetails and Options

  • PseudoInverse works on both symbolic and numerical matrices.
  • For a square matrix, PseudoInverse gives the MoorePenrose inverse.
  • For numerical matrices, PseudoInverse is based on SingularValueDecomposition.
  • PseudoInverse[m,Tolerance->t] specifies that singular values smaller than t times the maximum singular value should be dropped.
  • With the default setting Tolerance->Automatic, singular values are dropped when they are less than 100 times 10-p, where p is Precision[m].
  • For nonsingular square matrices M, the pseudoinverse M(-1) is equivalent to the standard inverse.
Introduced in 1988
| Updated in 2003