The Geometry of Rank Drop in a Class of Face-Splitting Matrix Products

arXiv2301.09826MaRDI QIDQ6508537

Erin Connelly, Rekha Thomas, Alperen Ali Ergur, Sameer Agarwal

Abstract: Given $kleq6$ points $(x_i,y_i)inmathbb{P}^{2}imesmathbb{P}^2$, we characterize rank deficiency of the $kimes9$ matrix $Z_k$ with rows $x_i^{o}potimes{y}_i^{o}p$ in terms of the geometry of the point configurations $x_i$ and $y_i$. While this question comes from computer vision the answer relies on tools from classical algebraic geometry: For $kleq5$, the geometry of the rank-drop locus is characterized by cross-ratios and basic (projective) geometry of point configurations. For the case $k=6$ the rank-drop locus is captured by the classical theory of cubic surfaces.

Has companion code repository: https://github.com/rekharthomas/rankdrop

This page was built for publication: The Geometry of Rank Drop in a Class of Face-Splitting Matrix Products

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6508537)