s1向量和矩阵范数/ Norms of vectors and matrices 为了误差的度量 >向量范数/ vector norms 定义R空间的向量范数‖·对任意xp蒲足下列条件: (1)‖x‖≥0;‖x‖=0x=0(正定性/ positive definite+/) (2)|axl‖l=al‖x‖对任意aeC(齐次性/ homogeneous+) (3)‖x+y‖s‖‖+‖(三角不等式/ triangle inequality 纔常用向量范数: H=∑|x :=1EIx ILIlp-2Ix, P'f =1 maxx 注:lim‖x,=‖xl I≤iSn§1 向量和矩阵范数 /* Norms of Vectors and Matrices */ —— 为了误差的度量 ➢ 向量范数 /* vector norms */ 定义 Rn空间的向量范数 || · || 对任意 满足下列条件： n x y R   , (1) || || 0 ; || || 0 0     x  x =  x = （正定性 /* positive definite */ ) (2) || x || | | || x ||    =   对任意  C (齐次性 /* homogeneous */ ) (3) || x y || || x || || y ||     +  + （三角不等式 /* triangle inequality */ ) 常用向量范数：  = = n i x xi 1 1 || || | |  = = n i i x x 1 2 2 || || | |  p n i p x p x i 1 / 1 || || =  | | =  || || max | | 1 i i n x x    =  注：  → lim || x || = || x || p p  