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BUILT-IN MATHEMATICA SYMBOL
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
, where p is Precision[m]. - For non-singular square matrices M, the pseudoinverse
is equivalent to the standard inverse.
Examplesopen all
Basic Examples (1)
A matrix has a pseudoinverse even if it is singular:
| In[1]:= |
| Out[1]= |  |
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