A new extension of the Frank matrix and its properties
Logic Journal of the IGPL, cilt.33, sa.6, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 33 Sayı: 6
- Basım Tarihi: 2025
- Doi Numarası: 10.1093/jigpal/jzaf039
- Dergi Adı: Logic Journal of the IGPL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
- Anahtar Kelimeler: determinant, factorization, Frank matrix, permanent
- Ankara Hacı Bayram Veli Üniversitesi Adresli: Evet
Özet
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.