This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 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. In[1]:= Out[1]//MatrixForm= In[2]:= Out[2]= In[3]:= For invertible matrices, the pseudoinverse is the same as the inverse. In[4]:= Out[4]= You can compute the pseudoinverse of a non-square matrix. In[5]:= Out[5]//MatrixForm= In[6]:= Out[6]//MatrixForm= Here is another pseudoinverse. In[7]:= Out[7]//MatrixForm= Here is another pseudoinverse. We use use Chop to get rid of the fuzz. In[8]:= Out[8]//MatrixForm= We use use Chop to get rid of the fuzz. In[9]:= Out[9]//MatrixForm=