{c}
{title2=$A^\dagger$}
{wiki=Moore–Penrose_inverse}

For a bounded operator $A:X\to Y$ between Hilbert spaces, the Moore–Penrose inverse maps admissible data to the unique minimum-norm least-squares solution. If $(\sigma_j,u_j,v_j)$ is a <singular system of a compact operator>, then
$$
A^\dagger y
=\sum_j\frac{\langle y,u_j\rangle}{\sigma_j}v_j
$$
on the data for which this series converges.

= Moore–Penrose generalized inverse operator
{c}
{synonym}


 Moore–Penrose inverse of an operator

ID: moore-penrose-inverse-of-an-operator