Subspace injections

Joel Tropp studies structured dimension reduction through the injectivity of random maps, motivated by fast low-rank approximation and least-squares regression. This viewpoint sharpens guarantees for sparse maps and gives exponential improvements for tensor-product dimension reduction. Experiments assess the resulting structured random matrices on synthetic problems and scientific applications. Joint work with Chris Camaño, Ethan Epperly, and Raphael Meyer, available as arXiv:2508.21189.