A~B→PAP=B →(PAP)'=BI →PrA(PT=B →PAI(PI)I=B →I(P)A(P)1=B →QA'Q1=Br(Q=(P) →AT~B7 his do Is pro ed by trial v of Print2Flash
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相似矩阵有许多共同的性质 可逆性 迹相同 相同 特征值 相同 秩相同 行列式 相同 等价 This docur nt is produced by trial vers of Print2Flash.Visit w
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为什么要考虑矩阵的相似变换？？ 相似矩阵具有许多共同的性质，因此，对于n阶方阵A, 我们希望在与A相似的矩阵中寻求一个较简单的矩阵。在研 究A的性质时，只需先研究这一较简单矩阵的同类性质。 若方阵A与一个对角阵1相似，则称方阵A可对角化。 记为A~A,并称1是A的相似标准形。 所谓对角化过程，就是找一个可逆矩阵C,使得C1AC 为对角矩阵
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n阶矩阵A与对角矩阵相似的条件 定理n阶矩阵A可对角化的充分必要条件是A有n 个线性无关的特征向量. 证明：必要性 若A~A 则存在n阶可逆矩 阵P,使得P1AP=A. his doc is nroduced by trial ver
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设P=(X1,X2,…,Xn) 显然，X≠0(i=1,2,…,m),且X,X2,,Xn线性无关. w6 P1AP=A→AP=PA →(AX,AX2,…,AXn)=(1X,2X2,…,nXn) →AX,=,X,(i=1,2,…,n) ed by trial v of Print2Flash Visi
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