  In this article, we propose a reduced basis method for parametrized
non-symmetric eigenvalue problems arising in the loading pattern optimization
of a nuclear core in neutronics. To this end, we derive a posteriori error
estimates for the eigenvalue and left and right eigenvectors. The practical
computation of these estimators requires the estimation of a constant called
prefactor, which we can express as the spectral norm of some operator. We
provide some elements of theoretical analysis which illustrate the link between
the expression of the prefactor we obtain here and its well-known expression in
the case of symmetric eigenvalue problems, either using the notion of numerical
range of the operator, or via a perturbative analysis. Lastly, we propose a
practical method in order to estimate this prefactor which yields interesting
numerical results on actual test cases. We provide detailed numerical
simulations on two-dimensional examples including a multigroup neutron
diffusion equation.
