RankRevealing.jl

This package defines methods for exact linear algebra over any numerical field. Our focus is on matrix decompositions that are rank-sensitive. That is, faster for low-rank matrices.

• RankRevealing.GeneralizedRankRevealing
• RankRevealing.PLUQ
• RankRevealing.basis
• RankRevealing.grr
• RankRevealing.intersection
• RankRevealing.left_rr
• RankRevealing.pluq
• RankRevealing.right_rr
• RankRevealing.simple_rr
• RankRevealing.sumspace

References

• [1] Jean-Guillaume Dumas, Clément Pernet, Ziad Sultan. "Simultaneous computation of the row and column rank profiles". In: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation. 2013, pp. 181–188.
• [2] Iago Leal de Freitas, Júlia Mota, João Paixão, Lucas Rufino. "Generalizing the Invertible Matrix Theorem with Linear Relations using Graphical Linear Algebra". 2025, preprint at arXiv:2502.16783v2.