2023/03/14 by Tae-Hyeong Kim, Kim, Taehyeong, Jeong-Hoon Ju +3
Computer Science · Mathematics · #14N07 #15A15 #62J07 #Advanced Optimization Algorithms Research #Commutative Algebra (math.AC) #FOS: Mathematics #Matrix Theory and Algorithms #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2303.07842
openalex publication_date 2023/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a new formula for the determinant of a 4 × 4 matrix. We approach via the sparse optimization problem and derive the formula through the Least Absolute Shrinkage and Selection Operator (LASSO). Our formula has the potential to advance understanding of the algebraic structure of determinants, such as an upper bound of the tensor rank, various notions to measure complexity, and effective computational tools in exterior algebras. We also address several numerical experiments which compare our formula with built-in functions in a computer-algebra system.