定理1正交向量组线性无关 证设a1,a2…,a,为正交向量组,且 K,a,+k k,a=0 则(a1k1a1+k2a2+…+k,a, =k1(a1,a1)+k2(x1,a2)+…+k,、(x1,a,) k1(an,a1)=0 1c1 >0 k1=0 同理:k2=k3 =0 1929 a线性无关返回 定理1 正交向量组线性无关 . 证 设1， 2，， s 为正交向量组，且 k11 + k2 2 ++ ks s = 0 ( ) s s 则 1，k11 + k2 2 ++ k  ( ) ( ) ( ) k   k   ks   s , , , = 1 1 1 + 2 1 2 ++ 1 ( , ) 0 , = k1 1 1 = ( , ) 0 , 0 ,  1 1   k1 = 0 , 同理：k2 = k3 == ks = , , , .  1  2   s 线性无关