用Schmidt正交化方法可得.
设 a1=(1,0,1,1),a2=(1,1,1,-1),a3=(1,2,3,1)
b1 = a1
b2 = a2 - (a2,b1)/(b1,b1)b1 = a2-(1/3)b1 = (2/3,1,2/3,-4/3)
b3 = a3 - (a3,b1)/(b1,b1)b1 - (a3,b2)/(b2,b2)b2
= a3 - 5/3b1 -10/11b2
= (-14/11,12/11,8/11,6/11).
b1,b2,b3 是与a1,a2,a3 等价的正交单位向量组.