Excluding a Line Minor via Design Matrices and Column Number Bounds for the Circuit Imbalance Measure

Daniel Dadush, Friedrich Eisenbrand, Rom Pinchasi +2

For a real matrix $A\in {\mathbb{R}}^{d\times n}$ with non-collinear columns, we show that $n\le O(d^4\hat{I}{º}_A)$ where $\hat{I}{º}_A$ is the \emph{circuit imbalance measure} of $A$. The cir…