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Math Help - eigen valuese of nXn of all 1 to have trangle of zeros form

  1. #1
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    eigen valuese of nXn of all 1 to have trangle of zeros form

    i have nxn matrice of 1 in each member
    i
    i need to make triangle of zeros on the bottom

    to find the polinomial

    how toma this triangle of zeos form
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: eigen valuese of nXn of all 1 to have trangle of zeros form

    Use the transformations (i) F_i\to F_i-F_1 for all i=2,\ldots,n and (ii) C_1\to C_1+C_2+\ldots+C_n .
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  3. #3
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    Re: eigen valuese of nXn of all 1 to have trangle of zeros form

    from you method i get this matrices
    it not eliminating the first coumn

    \begin{pmatrix}<br />
1+[n-2]\lambda &\lambda &\lambda  &\lambda \\ <br />
1-\lambda &-\lambda  &  0&0 \\ <br />
1-\lambda &0  &-\lambda  &0 \\ <br />
1-\lambda &0  &0  &-\lambda <br />
\end{pmatrix}
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: eigen valuese of nXn of all 1 to have trangle of zeros form

    First transformation:

    \begin{vmatrix} 1-\lambda & 1 & \ldots & 1\\ 1 & 1-\lambda & \ldots & 1 \\ \vdots&&&\vdots \\ 1 & 1 &\ldots & 1-\lambda\end{vmatrix}=\begin{vmatrix} 1-\lambda & 1 & \ldots & 1\\ \lambda & -\lambda & \ldots & 0 \\ \vdots&&&\vdots \\ \lambda & 0 &\ldots & -\lambda\end{vmatrix}

    Now, use the second one.
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