Definition:Combinatorial Matrix

Definition
A combinatorial matrix is a square matrix specified as:
 * $$a_{ij} = y + \delta_{ij} x$$

where $$\delta_{ij}$$ is the Kronecker delta.

In full, it can be written:


 * $$\begin{bmatrix}

x + y & y & \cdots & y \\ y & x + y & \cdots & y \\ \vdots & \vdots & \ddots & \vdots \\ y & y & \cdots & x + y \end{bmatrix}$$

Alternatively it can be expressed:
 * $$x \mathbf{I}_n + y \mathbf{J}_n$$

where:
 * $$\mathbf{I}_n$$ is the Identity Matrix of order $n$;
 * $$\mathbf{J}_n$$ is the square ones matrix of order $n$.