西安毛子科技大学XIDIANUNIVERSITY推广:老若欧氏空间V中向量αj,α2,,αm两两正交即(α;,α,)=0, i±j, i,j=l,2,.",m[ai +α, +.+a.' -|α' +[α?' + .+[am .则证:若(α,α,)=0,ij则 [a +α, ++αm ={(α,Zα,)il=Z(a,a,)+Z(a,α,)(α,α,)=α +, +.am§9.1 定义与基本性质 推广:若欧氏空间V中向量 1 2 , , , m 两两正交, 则 2 2 2 2 1 2 1 2 . + + + = + + + m m 证:若 ( , ) 0, i j = i j 则 2 1 2 1 1 ( , ) m m m i j i j = = + + + = 1 ( , ) ( , ) m m i i i j i i j = = + 2 2 2 1 2 1 ( , ) m i i m i = = = + + + ( , ) 0, , , 1,2, , i j 即 = = i j i j m