PUB - Publikationen an der Universität Bielefeld

In this note we consider band- or tridiagonal-matrices of order k whose elements above, on, and below the diagonal are denoted by b i, a i,c i. In the periodic case, i.e. b i+m=b i etc., we derive for k=nm and k=nm–1 formulas for the characteristic polynomial and the eigenvectors under the assumption that [Pi] m i=1 c ib i>0. In the latter case it is shown that the characteristic polynomial is divisible by the m–1-th minor, as was already observed by Rósa. We also give estimations for the number of real roots and an application to Fibonacci numbers.