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

Invariant Matsumoto metrics on homogeneous spaces