Upper bounds for determinants of symmetric positive-definite matrices (Q1326915)

Let \(A=(a_{ij})\) be an \(n \times n\) positive definite real symmetric matrix, let \(Q = \{(i_ v,j_ v):v = 1,\dots,s\}\) be a sequence of integers pairs such that \(1=i_ 1<\cdots<i_ s\), \(j_ 1 < \cdots < j_ s=n\) and \(i_{v+1} \leq j_ v+1\) for \(v=1, \dots,s-1\). The author obtains upper bounds for \(\text{det} A\) that depend only on \(a_{ij}\) for \((i,j) \in N(Q)\), where \[ N(Q) = \bigcup^ s_{v=1} \bigl \{(i,j):i,j \in \{i_ v,\dots,j_ v\}\bigr\}. \]