What are the Eigenvalues of the following matrix.
$c_i$ are reals.
I tried to compute the characteristic polynomial, but it is quite tedious.
2026-03-28 11:52:56.1774698776
Finding Eigenvalues of this matrix.
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Let $S=c_1+\ldots+c_n$ then $\det(A-\lambda I)= \begin{vmatrix} c_1-\lambda& c_1&\ldots&c_1\\ c_2& c_2-\lambda& \ldots&c_2\\ \ldots & \ldots & \ldots&\ldots\\ c_n& c_n& \ldots&c_n-\lambda\\ \end{vmatrix}=(S-\lambda)\begin{vmatrix} 1& 1&\ldots&1\\ c_2& c_2-\lambda& \ldots&c_2\\ \ldots & \ldots & \ldots&\ldots\\ c_n& c_n& \ldots&c_n-\lambda\\ \end{vmatrix}=\ldots $
Can you finish?