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PseudoInverse
PseudoInverse[
m
] finds the pseudoinverse of a rectangular matrix.
PseudoInverse works on both symbolic and numerical matrices.
For numerical matrices, PseudoInverse[
m
,
Tolerance
->
t
] specifies that singular values smaller than t times the maximum singular value are to be removed.
The default setting Tolerance
->
Automatic typically takes t to be  where  is the numerical precision of the input.
For non-singular square matrices  , the pseudoinverse  is equivalent to the standard inverse.
See the Mathematica book: Section 3.7.10.
See also: Inverse, SingularValues, Fit.
Related package: LinearAlgebra`Cholesky`.
Further Examples
The pseudoinverse of a matrix m, usually denoted by  , has the property that the sum of the squares of the entries of  is minimized, where  is an identity matrix of the appropriate size.
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For invertible matrices, the pseudoinverse is the same as the inverse.
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You can compute the pseudoinverse of a non-square matrix.
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Here is another pseudoinverse.
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Here is another pseudoinverse. We use use Chop to get rid of the fuzz.
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We use use Chop to get rid of the fuzz.
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Out[9]//MatrixForm= 
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