In this paper we consider invariant Matsumoto metrics which are induced by
invariant Riemannian metrics and invariant vector fields on homogeneous spaces
then we give the flag curvature formula of them. Also we study the special
cases of naturally reductive spaces and bi-invariant metrics. We end the
article by giving some examples of geodesically complete Matsumoto spaces

Moghaddam, H. R. Salimi