[線代] 一題證明題

[dkcheng (電磁霸主)]

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Let T be a linear operator from C  to itself and λ屬於 C . Let N(T) denote

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the null space of T. Prove that for every basis of C  with respect to which


T has an upper-triangular matrix, λ appears on the diagonal of the matrix

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of T precisely dim N((T-λI) ) times, or disprove it by giving a counter


example.


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