# physical meaning of hermitian matrix

Although I am not strong in advanced group theory and coxeter groups, but some how I sense some similarity between the following matrix I obtained and the geometries related to coxeter groups ... I am asking either for a discussion of this matrix form; if there exists similar form to it in the classes of known matrices (other than the general hermitian operator categorization)...

or if there are keywords that can reduce my research time...

the matrix is

\begin{bmatrix} 1 & {\rm e}^{j (d_1 - d_2)} & {\rm e}^{j (d_1 - d_3)} & \ldots & {\rm e}^{j (d_1 - d_N)} \\ {\rm e}^{j (d_2 - d_1)} & 1 & {\rm e}^{j (d_2 - d_3)} & \ldots & {\rm e}^{j (d_2 - d_N)} \\ {\rm e}^{j (d_3 - d_1)} & {\rm e}^{j (d_3 - d_2)} & 1 & \ldots & {\rm e}^{j (d_3 - d_N)} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ {\rm e}^{j (d_N - d_1)} & {\rm e}^{j (d_N - d_2)} & {\rm e}^{j (d_N - d_3)} & \ldots & 1 \end{bmatrix}

best regards and thanks for help