The matrix in the middle of the beginning part, i.e.,
$$ Q=\begin{bmatrix} \operatorname{diag}(s) & L \\ 0 & K \end{bmatrix} $$
In the context, $L$ is a $r$ by $c$ matrix. What is the meaning of $Q$ " is diagonal with a c-column border"? It seems it means the left part $\operatorname{diag}(s)$ is diagonal and meanwhile the right part$\begin{bmatrix} L\\ K\end{bmatrix}$ is of $c$ nonzero columns. In the context the author call $Q$ a "c-bordered diagonal matrix".
But is this formally defined in some linear algebra books? Or any reference?