Dirac-like Hamiltonians associated to Schr\"odinger factorizations

In this work, we have extended the factorization method of scalar shape-invariant Schr"o-din-ger Hamiltonians to a class of Dirac-like matrix Hamiltonians. The intertwining operators of the Schr"odinger equations have been implemented in the Dirac-like shape invariant equations. We have considered also another kind of anti-intertwining operators changing the sign of energy. The Dirac-like Hamiltonians can be obtained from reduction of higher dimensional spin systems. Two examples have been worked out, one obtained from the sphere ${\mathcal{S}}^2$ and a second one, having a non-Hermitian character, from the hyperbolic space ${\mathcal{H}}^2$.