Elsner, LudwigUniBi ; Redheffer, Raymond M.
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.
Elsner L, Redheffer RM. Remarks on band matrices. Numerische Mathematik. 1967;10(2):153-161.
Elsner, L., & Redheffer, R. M. (1967). Remarks on band matrices. Numerische Mathematik, 10(2), 153-161. doi:10.1007/BF02174148
Elsner, L., and Redheffer, R. M. (1967). Remarks on band matrices. Numerische Mathematik 10, 153-161.
Elsner, L., & Redheffer, R.M., 1967. Remarks on band matrices. Numerische Mathematik, 10(2), p 153-161.
L. Elsner and R.M. Redheffer, “Remarks on band matrices”, Numerische Mathematik, vol. 10, 1967, pp. 153-161.
Elsner, L., Redheffer, R.M.: Remarks on band matrices. Numerische Mathematik. 10, 153-161 (1967).
Elsner, Ludwig, and Redheffer, Raymond M. “Remarks on band matrices”. Numerische Mathematik 10.2 (1967): 153-161.
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