Moore-Penrose Pseudoinverse Calculator

Given an $m\times n$ real or complex matrix $A$, this application calculates the Moore-Penrose pseudoinverse $A^{+}$ of the matrix. $A^{+}$ is calculated from the singular value decomposition of $A$: \[ A = U\Sigma V^{H}, \] so $A^{+}$ is just \[ A^{+} = V\Sigma^{+}U^H, \] where $\Sigma^{+}$ is obtained by taking the reciprocal of each non-zero entry on the diagonal of $\Sigma$, leaving the zeros in place, and transposing the resulting matrix.

See Input Data for the description of how to enter matrix or just click Example for a simple example.

Pseudoinverse Calculator