Is there a name for square matrices whose rows and columns (and only these; indeed, the main diagonal entries always sum to $n \alpha,$ where $n$ is the size of the matrix, and $\alpha$ each entry of the form $a_{ii}$) sum to the same value?

For example, something like $$\begin{bmatrix} 2&1&0&1\\ 1&2&1&0\\ 0&1&2&1\\ 1&0&1&2 \end{bmatrix}.$$

PS. As it might help, an additional property that these matrices have is that they are at least persymmetric (that is in addition to the constancy of the row/column-sum above), although the antidiagonal need not be constant.

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    $\begingroup$ Not exactly what you asked, but a matrix with constant diagonals like your example is called a Toeplitz matrix. $\endgroup$ – Klaus Feb 15 at 17:55
  • $\begingroup$ @Klaus I didn't know that. That would mean the matrices I am interested in are a subclass of Toeplitz matrices. It's some progress, if you ask me! $\endgroup$ – Allawonder Feb 15 at 18:08
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    $\begingroup$ Maybe a "multiple of a doubly stochastic matrix"? $\endgroup$ – Teddan the Terran Feb 15 at 18:22
  • $\begingroup$ @TeddantheTerran What's a doubly stochastic matrix? Could you give an example too? $\endgroup$ – Allawonder Feb 15 at 18:46
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    $\begingroup$ @Allawonder No, but I meant that it is a multiple of a stochastic matrix: Divide all entries by 4, and call this matrix M. Then M is doubly stochastic, and 4M is your matrix. $\endgroup$ – Teddan the Terran Feb 15 at 21:59

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