A new generalization of the Frank matrix and its some properties
Baijuan Shi, Can Kizilates
article (Uluslararası, Hakemli) | Yazar(lar): Baijuan Shi, Can Kizilates | Yıl: 2024 | Dergi/Kurum: COMPUTATIONAL & APPLIED MATHEMATICS | İndeks: WOS.SCI | DOI: 10.1007/s40314-023-02524-2 | Anahtar Kelimeler: r-Frank matrix, Matrix factorization, Determinants, Inverses, Norms, Reciprocal matrix, Fibonacci numbers, Harm
Matrix theory is of great importance for the solution of some real-world problems and computational processes. Especially, some special type matrices and the linear algebraic properties of these matrices are considerably important for these computational processes. In this article, we propose a new r-Frank matrix, which is the general form of the Frank matrix, and other generalization of the Frank matrix. Then, we study its algebraic structure, some factorizations, determinant, inverse, and some norms. Moreover, we obtain miscellaneous linear algebra properties for the reciprocal matrix of the r-Frank matrix. Finally, to verify our results, as an interesting application, the mentioned above properties of the r -Frank matrix, whose entries are harmonic Fibonacci numbers, are presented.