Permanents and determinants of tridiagonal matrices with (s,t)-Pell numbers

2017 ◽  
Vol 12 ◽  
pp. 747-753
Author(s):  
Hasan Huseyin Gulec
Keyword(s):  
Pell Numbers ◽  
Tridiagonal Matrices

scholarly journals Integer powers of certain complex tridiagonal matrices and some complex factorizations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4715-4724
Author(s):  
Durmuş Bozkurt ◽  
Burcu Bozkurt-Altındağ
Keyword(s):  
General Expression ◽  
Tridiagonal Matrix ◽  
Fibonacci Polynomials ◽  
Pell Numbers ◽  
Tridiagonal Matrices

In this paper, we obtain a general expression for the entries of the rth power of a certain n x n complex tridiagonal matrix where if n is even, r ? Z or if n is odd, r ? N. In addition, we get the complex factorizations of Fibonacci polynomials, Fibonacci and Pell numbers.

On circulant like matrices properties involving Horadam, Fibonacci, Jacobsthal and Pell numbers

2021 ◽  
Vol 617 ◽  
pp. 100-120
Author(s):  
Enide Andrade ◽  
Dante Carrasco-Olivera ◽  
Cristina Manzaneda
Keyword(s):  
Pell Numbers

scholarly journals Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 870
Author(s):  
Diego Caratelli ◽  
Paolo Emilio Ricci
Keyword(s):  
Functional Analysis ◽  
Computer Algebra ◽  
Toeplitz Matrices ◽  
Test Cases ◽  
Recursive Procedure ◽  
Tridiagonal Matrices ◽  
Special Cases ◽  
The Matrix ◽  
Matrix Eigenvalues ◽  
Complex Valued

We show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toeplitz (in particular symmetric Toeplitz) matrices are included. The proposed method does not require the knowledge of the matrix eigenvalues and relies only on the relevant invariants which are determined, in a computationally effective way, by means of a dedicated recursive procedure. The considered technique has been validated through several test cases with the aid of the computer algebra program Mathematica©.

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