证:A为 Hermite矩阵→ A=UMU,A=dig(1,A2,…)Vx∈Cn x ax =x U AUx =(Ux)"A(Ux) J=Ux Ax =∑1|y i=1 →x"4x≥m.∑ly}=mny"y=mx"x →x" Ax<a∑|J2=1myy= H max min·x"xsx"Ax≤λmx:x"x返回 证: A为Hermite矩阵 1 2 , ( , , ) H A U U diag =   =    n n  xC x Ax H H H =  x U Ux ( ) ( ) H =  Ux Ux 2 1 | | n H i i i x Ax y  = =  2 min 1 | | n H i i x Ax y  =   y Ux = min H =  y y min H =  x x 2 max 1 | | n H i i x Ax y  =   max H =  y y max H =  x x x x x Ax x x H H H  min     max 