设V的正交基b1,b2 到 a1,a2 的过渡矩阵为
k11 k12
k21 k22
则有 a1=k11b1+k12b2
a2 = k21b1+k22b2
再由度量矩阵得
5 = (a1,a1) = k11^2+k12^2
4 = (a1,a2) = k11k21 + k12k22
5 = (a2,a2) = k21^2 + k22^2
可得过渡矩阵为
1 2
2 1