The Moore-Penrose Pseudoinverse is a generalization of the matrix inverse for any matrix, not just square invertible ones. It is denoted as \(A^+\).

The Process (using SVD):

The most stable way to compute the pseudoinverse is via Singular Value Decomposition (SVD), where \(A = U \Sigma V^T\).

1. Decompose A into its SVD components: \(U\), \(\Sigma\), and \(V\).
2. Find the pseudoinverse of \(\Sigma\), denoted \(\Sigma^+\). This is done by taking the reciprocal of each non-zero singular value on the diagonal and then transposing the resulting matrix.
3. Assemble the final pseudoinverse using the formula:
   \(A^+ = V \Sigma^+ U^T\)

This calculator performs these steps to find the pseudoinverse for any given matrix.