In this paper we consider invariant Matsumoto metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces, and 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.
"Invariant Matsumoto metrics on homogeneous spaces." Osaka J. Math. 51 (1) 39 - 47, January 2014.