[Everyday Mathematics]20150109
2015-01-05 20:39
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设 $A$ 是 $n$ 阶复方阵, 其特征多项式为 $$\bex f(\lm)=(\lm-\lm_1)^{n_1}\cdots(x-\lm_s)^{n_s}, \eex$$ 其中 $\lm_i$ 互不相同. 再设 $$\bex V=\sed{B\in C^{n\times n};\ AB=BA}. \eex$$ 试证: $\dim V=n_1^2+\cdots+n_s^2.$
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