81 Norms of Vectors and Matrices-Matrix Norms >矩阵范数/ matrix norms 定义Rm空间的矩阵范数‖·对任意A,B∈满足: (1)‖A‖0;‖A=0分A=0(正定性/ positive definite*) (2)|aA‖=|al·A对任意aEC(齐次性/ homogeneous+) (3)‖4+BsA+‖B‖(三角不等式/ triangle inequality) (4)‖AB|S‖A‖·‖B‖(相容/ consistent!当m=n时) When you have to analyze the error bound of AB- imagine you doing it without a consistent matrix norm§1 Norms of Vectors and Matrices – Matrix Norms ➢ 矩阵范数 /* matrix norms */ 定义 Rmn空间的矩阵范数 || · || 对任意 满足： m n A B R  ,  (1) || A||  0 ; || A|| = 0  A = 0 （正定性 /* positive definite */ ) (2) || A|| = | |  || A|| 对任意  C (齐次性 /* homogeneous */ ) (3) || A+ B ||  || A|| + || B || （三角不等式 /* triangle inequality */ ) (4)* || AB ||  || A || · || B || （相容 /* consistent */ 当 m = n 时) In general, if we have || AB ||  || A || · || B || , then the 3 norms are said to be consistent. Oh haven’t I had enough of new concepts? What do I need the consistency for? When you have to analyze the error bound of AB – imagine you doing it without a consistent matrix norm…