Does this type of matrix with the same diagonals have a name?

Question

Given real numbers $x_1, x_2, x_3, \dots, x_n$, we define the real symmetric matrix

$$ \begin{pmatrix} \color{red}{x_1} & \color{red}{x_1} & \color{red}{x_1} & \cdots & \color{red}{x_1} \\ \color{red}{x_1} & \color{blue}{x_2} & \color{blue}{x_2} & \color{blue}{\cdots} & \color{blue}{x_2} \\ \color{red}{x_1} & \color{blue}{x_2} & \color{green}{x_3} & \cdots & \color{green}{x_3} \\ \color{red}{\vdots} & \color{blue}{\vdots} & \color{green}{\vdots} & \ddots & \\ \color{red}{x_1} & \color{blue}{x_2} & \color{green}{x_3} & \cdots & x_n \end{pmatrix} $$

So this matrix has all diagonals of the form $x_1, x_2, x_3, \dots, x_n$.

Does this matrix have a name? If not, I am curious if anything can be said about its eigenvalues and eigenvectors.

Answer 1

This matrix is known with the name MIN matrix and is well studied in (Kilic & Arican, 2019, Studying new generalizations of Max-Min matrices with a novel approach) and in (Mattila & Haukkanen, 2016, Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods).