通常的力学、电动力学及相对论教材中都是用时空的均匀各向同性一句话来说明相对论变换必须是线性变换. 在实际教学中，很多学生都对这种说法表示难以理解. 而物理科学就是要用严谨的数学来说明简单的物理思想. 本文利用狭义相对论的两个基本原理及时空均匀各向同性严格证明惯性坐标系之间的相对论坐标变换一定是线性变换. 

 In most textbooks on mechanics, electrodynamics and relativity, the linear transformation between inertial frames is usually argued by the homogeneity and isotropy of spacetime. During teaching this subject, some students cannot understand this simple argument. After all, the science of physics should be explained with solid mathematics. This paper provides a solid mathematical proof of linear transformation between inertial frames based on the two postulates of special relativity and the homogeneity and isotropy of spacetime.