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

1. ## 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

2. ## 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) $C_1\to C_1+C_2+\ldots+C_n$ .

3. ## 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

$\begin{pmatrix}
1+[n-2]\lambda &\lambda &\lambda &\lambda \\
1-\lambda &-\lambda & 0&0 \\
1-\lambda &0 &-\lambda &0 \\
1-\lambda &0 &0 &-\lambda
\end{pmatrix}$

4. ## 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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