A new extension of the Frank matrix and its properties
Logic Journal of the IGPL, vol.33, no.6, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 33 Issue: 6
- Publication Date: 2025
- Doi Number: 10.1093/jigpal/jzaf039
- Journal Name: Logic Journal of the IGPL
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
- Keywords: determinant, factorization, Frank matrix, permanent
- Ankara Haci Bayram Veli University Affiliated: Yes
Abstract
Motivated by the most recent literature, in this paper, we define a new generalization of the Frank matrix that we will call the geometric Frank matrix. In addition to considering some of its algebraic properties, we obtain its factorization, its determinant, as well as a recurrence relation for its permanent. Upper bounds are set for the spectral norm. We also investigate similar properties for the Hadamard inverse of the geometric Frank matrix. Finally, we provide a MATLAB-R2023a code to facilitate the computation of the permanent of an arbitrary geometric Frank matrix.