= Determinant of the minimum-index matrix
{title2=$\det(\min(i,j))_{i,j=1}^n=1$}
Let $L$ be the <triangular matrix> with $L_{ij}=1$ for $j\leq i$ and zero otherwise. Then $(LL^T)_{ij}=\min(i,j)$ and $\det L=1$, so the <determinant> of $LL^T$ is one. More generally, for $0=t_0<t_1<\cdots<t_n$, the <matrix> with entries $\min(t_i,t_j)$ factors as $L\operatorname{diag}(t_k-t_{k-1})L^T$ and has <determinant> $\prod_k(t_k-t_{k-1})$. This is the finite-dimensional structure behind the <Brownian covariance kernel>.
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