Projection of angular momentum via linear algebra

Projection of many-body states with good angular momentum from an initial state is usually accomplished by a three-dimensional integral. We show how projection can instead be done by solving a straightforward system of linear equations. We demonstrate the method and give sample applications to ${}^{48}$Cr and ${}^{60}$Fe in the $pf$ shell. This new projection scheme, which is competitive against the standard numerical quadrature, should also be applicable to other quantum numbers such as isospin and particle number.