TY  - JOUR
AB  - 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.
DA  - 1967
DO  - 10.1007/BF02174148
LA  - eng
IS  - 2
M2  - 153
PY  - 1967
SN  - 0029-599X
SP  - 153-161
T2  - Numerische Mathematik
TI  - Remarks on band matrices
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-17749053
Y2  - 2024-11-22T03:52:08
ER  -