第三章 矩阵分析 一、矩阵序列 二、矩阵级数 三、矩阵函数 四、矩阵的微分和积分 五、矩阵分析应用举例 理工大学 This document is produced by trial version of Print2Flash. Visit www.print2flash.com for more information
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矩阵序列与矩阵级数 矩阵的谱与谱半径 ·矩阵的谱半径：矩阵范数在特征值估计中的应用 设AeC”,方，元为A的个特征值，称集合 {02…2,} 为矩阵A的谱，记作G(4) 称 p(A)=max 为矩阵A的谱半径 This documentis produced bytrialversinofPVisit www.prinashcmformoreinfomio
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3.1.矩阵序列 定义1设矩阵序列{A)}∈Cm”，其中 A=(a,)m,如果mn个数列 1ima,=a,i=1,2,…,mj=1,2,,n k)0 则称矩阵序列{A}收敛于A=(a,)mn或称A 为矩阵序列{A)}的极限。记为 IimA)=A或A→A(k→0) 否则称为发散。 This docur at is produced by trial versi on of Print2Flash.Visit www.print2flash.com for mo nformatio
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例 如果设4=[a,]eC22,其中 ,=+1 ,a:=r0<r<) =r>1),a=- k2+k 那么 s作 Print2Flash
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定理3.1矩阵序列{A}收敛于A的充分 必要条件是 lim44)4=0 k)0 其中为任意一种矩阵范数。 证明取矩阵范数 14L=2a i=1i=1 必要性：设 lim 4()=A=(an) →00 his doc uced by trial ver of Print2Flash.Visit w
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