由定义可知，矩阵级数三“收敛的充要条 件是mn个数项级数 i=1,2,…,m;j=1,2,…,n 都收敛。 进一步，如果mn个数项级数 a112j=12.m k=0 d by trial
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都绝对收敛，则称矩阵级数 A=A+A++A+ k=0 绝对收敛→收敛 绝对收敛。 例设有矩阵级数 4,其中 0 π 2 又 ∈C22,即有4个数项级数 0 (k+1)(k+2) This docu t is produced by trial vers of Print2Flash.Visit www.print2flash.com
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k=0 0 兰= (k+1k+2) 那么矩阵级数 2Ak)=A0+A四++A+ 是否收敛，收敛到多少？ his de ed by trial
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定理3.4 设A)=[a,]∈Cm,则矩阵 级数 4=++++ 绝对收敛的充要条件是正项级数 4=4+4++4+ 收敛，其中‖A为任意一种矩阵范数。 证明取矩阵范数 his doc ced by tris
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4Ln=22a, 那么对每一对i,j都有 4L≥a,例 因此如果 三l=4L+4ol++4儿+ 收敛，则对每一对i,广，数项级数 hlb+e++b+… Iby trial of Print2Flash.Visit
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