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PseudoInverse

PseudoInverse[m]
finds the pseudoinverse of a rectangular matrix.

MORE INFORMATION

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.

Basic Examples (1)

A matrix has a pseudoinverse even if it is singular:

Generalizations & Extensions (1)

Applications (1)

Properties & Relations (3)

Inverse LeastSquares Fit SingularValueDecomposition SingularValueList

Advanced Matrix Operations

Linear Systems

Matrices and Linear Algebra

Matrix-Based Minimization

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