The Lorentz transformations:

δs = (δs' + βδt')(1-β²)^-1/2

δt = (δt' + βδs')(1-β²)^-1/2

δs' = (δs - βδt)(1-β²)^-1/2

δt' = (δt - βδs)(1-β²)^-1/2

In the transformations β = δs_r/δt_r is the velocity between the unprimed and the primed Lorentz reference frames, where δs_r is measured in the same direction as δs. In contrast the direction of δs' is reflected so that δs_r = -δs'_r (numerically only) and, hence, -δs_r'/δt'_r = -β. However, measurements may be recorded as positive by applying the same convention in both frames, hence, δs' and δs'_r would not be assigned a minus sign. Either way will not affect the results of the transformation from one hyperbolic vector space to another provided signs are consistently applied to all measurements and the results interpreted accordingly.