PseudoInverse

PseudoInverse[m]

finds the pseudoinverse of a rectangular matrix.

Details and Options

  • PseudoInverse works on both symbolic and numerical matrices.
  • For a square matrix, PseudoInverse gives the Moore–Penrose 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 non‐singular square matrices M, the pseudoinverse M(-1) is equivalent to the standard inverse.

Examples

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Basic Examples  (1)

A matrix has a pseudoinverse even if it is singular:

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Scope  (2)

Generalizations & Extensions  (1)

Options  (1)

Applications  (1)

Properties & Relations  (3)

See Also

Inverse  LeastSquares  Fit  SingularValueDecomposition  SingularValueList

Tutorials

Introduced in 1988
(1.0)
| Updated in 2003
(5.0)