V ={AXXeP"), V, ={X|XeP",AX=0西要毛子科技大枣三XIDIAN UNIVERSITY下证V,是P"的子空间。： A0=0, : 0eV,+0又对 Vα,βV,VkeP,有Aα = 0,Aβ = 0,从而有 A(α+β)= Aα+Aβ=0+0=0A(kα) = kAα = k0 = 0.. α+βeV2, kαeV,故 V,是 P"的子空间.2 A V 0 0, 0 =     A A   = = 0, 0, 又对 2      , , , V k P 有 从而有 A A A ( ) 0 0 0     + = + = + = A k kA k ( ) 0 0   = = = 2 2  +      V k V , 故 是 的子空间. n V2 P 下证 是 的子空间. n V2 P , 1 2 , 0 n n V AX X P V X X P AX             =  =  =