若向量组$alpha_{1},alpha_{2},alpha_{3},alpha_{4}$线性无关，则向量组$alpha_{1}-alpha_{2},alpha_{2}-alpha_{3},alpha_{3}-alpha_{4},alpha_{4}-alpha_{1}$也线性无关.

因为$(alpha_{1}-alpha_{2})+(alpha_{2}-alpha_{3})+(alpha_{3}-alpha_{4})+(alpha_{4}-alpha_{1})=0$,所以$alpha_{1}-alpha_{2},alpha_{2}-alpha_{3},alpha_{3}-alpha_{4},alpha_{4}-alpha_{1}$ 线性相关.