任取αeVnV,即αeV且αeV2由αeV,必有βep",使Aβ=α.由αV,有Aα= 0.从而 α= Aβ= A’β= A(Aβ)= Aα=0.:. Vnv, ={0)所以 p"=V④V2.86.7子空间的直和A§6.7 子空间的直和 = V V 1 2 0 2 由 = V A , 0. 有 1 , . n 由 = V P A 必有 , 使 任取 1 2 1 2 V V V V , 即 且 . 2 从而 = = = = = A A A A A ( ) 0. 1 2 . n 所以 P V V =