设a1,a2,a3是三维空间R^3的一组基,则有基a1,1/2a2,1/3a3到基a1-a2,a2+a3,a3+a1的过渡矩阵为

(a1,1/2a2,1/3a3)=(a1,a2,a3)P1P1=1 0 00 1/2 00 0 1/3(a1-a2,a2+a3,a3+a1)=(a1,a2,a3)P2P2=1 0 1-1 1 00 1 1所以 (a1-a2,a2+a3,a3+a1)=(a1,a2,a3)P2 = (a1,1/2a2,1/3a3)P1^-1P2过渡矩阵为P1^-1P2=1 0 1-2 2 00 3 3...