The dispersion tensor for linear wave propagation in an arbitrary number of moving plasma species is derived using an approach that is based on Lorentz transformations. This approach requires less computational effort than the direct approach, in which the equation of motion for each plasma species is linearized about an equilibrium state with nonzero velocityvs. As a specific example, the effects of an axial magnetic field and transverse beam temperature on the collisionless Weibel instability are studied.