Positive Integer Powers OF Symmetric(0,1)-Heptadiagonal Matrix

Journal of Applied Mathematics, 2020

Tridiagonal matrices appear frequently in mathematical models. In this paper, we derive the positive integer powers of special tridiagonal matrices of arbitrary order.

Applied Mathematics and Computation, 2008

In this paper, we derive a general expression for the entries of the qth power ðq 2 NÞ of the n  n complex tridiagonal matrix tridiag n ða 1 ; a 0 ; a À1 Þ for all n 2 N, in terms of the Chebyshev polynomials of the second kind.

2014

In this paper, we derive the general expression of the sth (s in N if n is odd; s in Z if n is even) power of some tridiagonal matrices.

Journal of Informatics and Mathematical Sciences, 2019

In this paper, we derive a general expression for the entries of the $r$th power $\left( r\in \mathbb{N} \right) $ of one type of the $n\times n$ complex pentadiagonal matrix for all $n \geq 4( r-1)$, in terms of binomial coefficients.

Applied Mathematics and Computation, 2013

In this paper, we firstly present a general expression for the entries of the th r   N r  power of certain-square n are complex tridiagonal matrix, in terms of the Chebyshev polynomials of the first kind. Secondly, we obtain two complex factorizations for Fibonacci and Pell numbers. We also give some Maple 13 procedures in order to verify our calculations.

In this study we derive the general expression for the entries of the qth power (qEN) for one type of even order symmetric pentadiagonal matrices.

2014

In this paper, we derive the general expression of the r−th power for some n-square complex tridiagonal matrices.Also one type is given eigenvalues and eigenvectors of complex anti-tridiagonal matrices Additionally, we obtain the complex factorizations of Fibonacci polynomials.

arXiv (Cornell University), 2014

In this paper, we derive the general expression of the r−th power for some n-square complex tridiagonal matrices.Also one type is given eigenvalues and eigenvectors of complex anti-tridiagonal matrices Additionally, we obtain the complex factorizations of Fibonacci polynomials.

Applied Mathematics and Computation, 2009

In this paper, we present an eigendecomposition of a tridiagonal matrix. Tridiagonal matrix powers and inverse are derived. As consequence, we get some relations verified by the coefficients of the inverse and the powers of a tridiagonal matrix.

2013

This paper shows how to obtain a simple closed form for the elements of a triangular matrix raised to the nth power.