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We show that the reciprocal maximal likelihood degree (rmld) of a diagonallinear concentration model $\mathcal L \subseteq \mathbb{C}^n$ of dimension $r$is equal to $(-2)^r\chi_M( \textstyle\frac{1}{2})$, where $\chi_M$ is thecharacteristic polynomial of the matroid $M$ associated to $\mathcal L$. Inparticular, this establishes the polynomiality of the rmld for general diagonallinear concentration models, positively answering a question of Sturmfels,Timme, and Zwiernik.

Reciprocal maximum likelihood degrees of diagonal linear concentration models