finding eigen values for nXn matrices

**transgalactic** · June 25th 2011, 10:27 AM

i dont know ho to make a trangle of zeros below the diagonal
if i subtract the first column from the rest i get zeros below the diagonal.
but the first column remain intact.

what to do with it
?

**FernandoRevilla** · June 25th 2011, 12:13 PM

Using the trasformations (i) $F_i\to F_i-F_1$ for all $i=2,\ldots,n$ and (ii) $C_1\to C_1+C_2+\ldots+C_n$ :

$\det (A-\lambda I)=\begin{vmatrix} -\lambda & \;\;a & \ldots & \;\;a\\ \;\;a &-\lambda & \ldots & \;\;a \\ \vdots&&&\vdots \\\;\; a & \;\;a &\ldots & -\lambda\end{vmatrix}=\ldots=[(n-1)a-\lambda](-a-\lambda)^{n-1}$

**transgalactic** · June 25th 2011, 01:49 PM

thanks

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