2024/09/19 by Youming Qiao, Qiao, Youming, Xiaorui Sun +1
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2409.12457
openalex publication_date 2024/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Left-right and conjugation actions on matrix tuples have received considerable attention in theoretical computer science due to their connections with polynomial identity testing, group isomorphism, and tensor isomorphism. In this paper, we present polynomial-time algorithms for computing canonical forms of matrix tuples over a finite field under these actions. Our algorithm builds upon new structural insights for matrix tuples, which can be viewed as a generalization of Schur's lemma for irreducible representations to general representations.