Is there a name for a square matrix with constant diagonal and off-diagonal elements? I am interested in real symmetric matrices of the form:
$$\mathbf{M} = \begin{bmatrix}
a & t & t & \cdots & t \\
t & a & t & \cdots & t \\
t & t & a & \cdots & t \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
t & t & t & \cdots & a \text{ } \text{ } \\
\end{bmatrix}.$$
This is a simple matrix form where the diagonal elements have a constant value $a \in \mathbb{R}$ and the off-diagonal elements have a constant value $t \in \mathbb{R}$.  Some useful special cases of this matrix form are the centering matrix and the equicorrelation matrix.  (This matrix form is also a particular case of the Toeplitz matrix, but it is much simpler than that general form.)
Question: Does this matrix form have a name?

In old statistics literature, these are sometimes called completely symmetric matrices.  I have made a light effort to revive the term in my writing or teaching (which is usually a combinatorial context).
