1.2相似对角化 定义：设A,B∈Cm”,若存在PeC,"使得 PAP=B,则称A与B相似，记为A~B P称为相似变换阵
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注1.一般来说，与n阶矩阵A相似的矩阵 可能不只一个 因为对于任意的n阶可逆矩阵P，都有 A~P-AP: 对于可逆矩阵P,A~B,=PAP, 对于可逆矩阵卫，A~B2=P2AP, ●●● P不同，则B可能不同， 但都有A~B. his docu is produced by trial vers of Print2Flash.Visit www.print2flash.com for more information
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2.和数量矩阵相似的矩阵只有它自身 设A 则对于任意的可逆矩阵P p-wip-al- by tria
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相似的性质 1.反身性：A~A(AI=A) 2.对称性：A~B→B~A (A~B→PAP=B→A=(P)BP) 3.传递性：A~B,B~C→A~C (PAP=B,PBP =C,PPAP P=C, (P)A(E)=C,而PD是可逆的，A~C) his doc is produced by trial vers of Print2Flash.Visit www.print2flash.com
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4.若A~B,则A与B的特征值相同反之不对 PAP=B →12I-B|=|2I-P-AP| =P-AIP-P-AP =P-(2I-A)P| =P-1|2I-A||P =|九I-A |I-A=|I-B| This doc nt is produced by trial version of Print2Flash.Visit www.print2flash.c
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