首先：?是1-1对应的，: ker = (αp(α) = 0,αe V) = (α α** = 0,α e V)若a = xe +x,e, +...+x,en e kerp,则对Vf V*,α*(f)=0, 即,f(α)=0.又 α=Ef(α)6;,:. f(α) =f(α)f(s,)=0由f的任意性，f.(α) = 0,i = 1,2,...,n.即.: α = 0.x; = f(α) = 0,故?是单射.$10.2对偶空间区区§10.2 对偶空间 首先：  是1-1对应的， ** ker { ( ) 0, } { 0, }         = =  = =  V V 1 1 2 2 ker , n n 若      = + + +  x x x 则对 , 即, * **   = f V f , ( ) 0  f ( ) 0.  = ( ) , ( ) ( ) ( ) 0 i i i i 又       =  = =   f f f f 由 f 的任意性， ( ) 0, 1,2, , . i f i n  = = ( ) 0, i i 即 x f = =  故 是单射.  =  0