Integer Powers of Complex Tridiagonal and Anti-Tridiagonal Matrices (original) (raw)

Integer powers of complex tridiagonal 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.

Positive integer powers of certain complex tridiagonal matrices

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.

Powers of tridiagonal matrices with constant diagonals

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.

Positive integer powers of certain tridiagonal matrices

Applied Mathematics and Computation, 2008

In [J. Rimas, On computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of even order-I, Appl. Math. Comput. 168 (2005) 783-787] and [J. Rimas, On computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of odd order-I, Appl. Math. Comput. 171 (2005) 1214-1217] Rimas derived a general expression for the entries of the qth power ðq 2 NÞ of the n  n real symmetric tridiagonal matrix tridiag n ð1; 0; 1Þ for all n 2 N. In this paper, we present an extension of that interesting work, deriving a similar expression for the entries of the qth power ðq 2 NÞ of the n  n Hermitian tridiagonal matrix tridiag n ða 1 ; a 0 ; a 1 Þ for all n 2 N.

On the powers and the inverse of a tridiagonal matrix

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.