Question

设有线性无关的向量组:a1=(1 1 1 1),a2=(3 3 -1 -1),试将a1,a2,a3正交化.

Answer 1

1=a1/|a1|=(1/4,1/4,1/4,1/4)

b=a2-r1=(3,3,-1,-1)‘-[（1/4）*3+(1/4)*3-(1/4)*(-1)-(1/4)(-1)](1,1,1,1)'=(2,2,-2,-2)

r2=b/|b|=4(1/4,1/4,-1/4,-1/4)

c=a3-r1-r2=(72,64,-88,-96)

r3=c/|c|=(9,8,-11,-12)/根号410