当Ax=λx => A^(-1)Ax=A^(-1)λx
=>Ix=λA^(-1)x
=>1/λ x=A^(-1)x
当A^(-1)x=1/λ x
证明同上
得证
如何证明λ是矩阵A的特征是当且仅当1/λ是A的逆(矩)阵的特征值?
如何证明λ是矩阵A的特征是当且仅当1/λ是A的逆(矩)阵的特征值?
数学人气:830 ℃时间:2019-11-05 01:18:01
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