匹明g 代入下式 ∑a+br=2a+hla+b 则 ∑a+bf=2a+la+hjf ≤∑ala+b5+2ba+b5 对上式由Holder2不等式可得
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之a+r≤②ara+Ar +∑b)(∑a+b) =I2b+2br)2a+h) 此不等式两端同除以（∑a+b)°，根据 1+1=1可得 a+)y≤a)+b)
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几种常用的范 定义：设向量 a=[a,a,…,an],对任 意的数p≥1，称 la,=21ar)% 为向量a的p-范数。 (1)1-范数4，=立al (2)2一范数（也称为欧氏范数） a=(=(a"a) (3)0-范数l4l.=maxla. d by trial
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定理在向量空间C中，向量范数满足 iml2=X。 证明当X=0时，结论显然成立。设X≠0，x=mar, 则 M,-②传- 因为 kPs∑xP≤x 所以 lim =kl=max= uced by trial ver of Print2Flash.Visit
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利用向量范数可以构造新的向量范数。 例1设·‖是Cm上的向量范数，且 A∈Cmxn rank(A)=n,则由 lxl=AL,x∈C” 所定义的是C"上的向量范数
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