Positive integer powers of certain tridiagonal matrices

摘要

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 (q∈N) of the n×n real symmetric tridiagonal matrix tridiagn(1,0,1) for all n∈N. In this paper, we present an extension of that interesting work, deriving a similar expression for the entries of the qth power (q∈N) of the n×n Hermitian tridiagonal matrix tridiagn(a1,a0,a1¯) for all n∈N.