Positive integer powers of certain tridiagonal matrices
The author presents an extension of previous works of \textit{J. Rimas} [Appl. Math. Comput. 168, No. 2, 783--787 (2005; Zbl 1082.65523), ibid. 171, No. 2, 1214--1217 (2005; Zbl 1090.65048)], where he derived a general expression for the entries of the \(q\)th power (\(q\in\mathbb {N}\)) of the \(n\times n\) real symmetric tridiagonal matrix \(\text{tridiag}_n(1,0,1)\) for all \(n\in\mathbb {N}\). He derives a similar expression for the entries of the \(q\)th power \((q\in\mathbb {N})\) of the \(n\times n\) Hermitian tridiagonal matrix \(\text{tridiag}_n(a_1,a_0,\overline{a_1})\).
scientific article; zbMATH DE number 5318702
scientific article