# Is the linearity of transformation of intervals postulate in SR? [duplicate]

Let $O$ and $\overline{O}$ be inertial frames, $A$ and $B$ be events, the interval between $A$ and $B$ be $(\Delta t, \Delta x, \Delta y, \Delta z)$ in $O$ and $(\overline{\Delta t}, \overline{\Delta x}, \overline{\Delta y}, \overline{\Delta z)}$ in $\overline{O}$.
Is the linearity of the correspondence between $(\Delta t, \Delta x, \Delta y, \Delta z)$ and $(\overline{\Delta t}, \overline{\Delta x}, \overline{\Delta y}, \overline{\Delta z)}$ a postulate in the special relativity theory?