I would like to compute the determinant of a matrix with the following structure: \begin{equation} \begin{pmatrix} D_1 & l_1 & l_1 &\cdots & l_1 \\ l_2 & D_2 & l_2 &\cdots & l_2 \\ l_3 & \cdots & D_3 &\cdots & l_3 \\ l_4 & \cdots & l_4 & D_4 & l_4 \\ l_5 & \cdots & \cdots & l_5 & D_5 \\ \end{pmatrix} \end{equation} That is, it is constant on each line apart from the diagonal. $l_i, D_i \in \mathbb R^+$.
Is there a way to make use of such symmetric structure to simplify the calculation of the determinant?
from Hot Weekly Questions - Mathematics Stack Exchange
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