  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 ${\cal S}^2$ and a second one, having a non-Hermitian character,
from the hyperbolic space ${\cal H}^2$.
