Given a symmetric matrix $A\in\mathbb{R}^{n\times n}$ with positive entries and zero diagonal, is it always possible to construct a high-dimensional configuration in Euclidean space, such that these coordinates give rise to distances from $A$? (high-dimensional configuration implies dimensionality at most $n-1$)
If this is generally not possible, what would be the conditions that have to be met in order to achieve a high-dimensional configuration giving rise to distances in $A$?