Optimal unit triangular factorization of symplectic matrices

2021/07/31 by Pengzhan Jin, Jin, Pengzhan, Zhangli Lin +3 · 3 citations
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Matrix Theory and Algorithms #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2108.00223

openalex publication_date 2021/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any symplectic matrix can be factored into no more than 5 unit triangular symplectic matrices, moreover, 5 is the optimal number. This result improves the existing triangular factorization of symplectic matrices which gives proof of 9 factors. We also show the corresponding improved conclusions for structured subsets of symplectic matrices. This factorization further provides an unconstrained optimization method on 2d-by-2d real symplectic group (a 2d²+d-dimensional Lie group) with 2d²+3d parameters.

Cited by

• Parametric Factorization of Matrices
• Symplectic convolutional neural networks
• Untriangular factorization of holomorpic symplectic matrices

Related

• Unit triangular factorization of the matrix symplectic group
• Numerical stability of the symplectic LL^T factorization
• Untriangular factorization of holomorpic symplectic matrices
• On computing the symplectic LL^T factorization
• Factorization of symplectic matrices into elementary factors