Maximizing Determinants under Matroid Constraints

Vivek Madan, Aleksandar Nikolov, Mohit Singh +1

Given vectors $v_1,\dots ,v_n\in {\mathbb{R}}^d$ and a matroid $M=([n],I)$, we study the problem of finding a basis $S$ of $M$ such that $\det ({\sum }_{i\in S}{v}_i{v}_i^{\top })$ is maximized…