We derive a relativistic mass tensor (dyadic or matrix) whose origin and properties have a direct geometric interpretation in terms of projection operators related to the particle’s world line and local inertial frame in Minkowski space, yet whose eigenvalues are simply the longitudinal (ml) and the transverse (mt) mass. Writing the noncovariant equations of motion (EOM) for a point particle in terms of this mass tensor bridges the gap between the compact but sterile form of the Lorentz covariant EOM and the usual (‘‘unwieldy’’) noncovariant EOM in whichmlandmtappear. General expressions for 3‐ and 4‐space mass (inverse mass) tensors are presented in terms of the system Lagrangian (Hamiltonian).