(3)(α(α+ β),o(α+ β))=(α+β,α+β),把(3)展开得，(α(α),(α) + 2(α(α),α(β))+(α(β),(β)=(α,α)+2(α,β)+(β,β)再由(1)(2)即得,(α(α),α(β)=(α, β)α是正交变换$9.4正交变换区区§9.4 正交变换 把(3)展开得， (            ( ), ( ) 2 ( ), ( ) ( ), ( ) ) + + ( ) ( ) = + + ( , ) 2( , ) ( , )       再由(1)(2)即得， (      ( ), ( ) ( , ) ) = (          ( ), ( ) ( , ), + + = + + ) (3)   是正交变换．