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Math Help - Classify up to similarity all nxn nilpotent matrices over K for n<=5

  1. #1
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    Classify up to similarity all nxn nilpotent matrices over K for n<=5

    As the title says, how do I classify up to similarity all nxn nilpotent matrices over K for n less than or equal to 5? I have no clue, any thoughts?
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  2. #2
    Super Member girdav's Avatar
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    Re: Classify up to similarity all nxn nilpotent matrices over K for n<=5

    Maybe the case n=2 can give you ideas. Let A be a 2\times 2 nilpotent matrix. Either A=0 or A^2=0. If A\neq 0, let x be such that Ax\neq 0. Then (x,Ax) forms a basis of K^2, and in this basis, A looks like \begin{pmatrix}0&1\\0&0\end{pmatrix}.
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