Remarks on band matrices

Elsner L, Redheffer RM (1967)
Numerische Mathematik 10(2): 153-161.

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Abstract / Bemerkung
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.
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Zeitschriftentitel
Numerische Mathematik
Band
10
Zeitschriftennummer
2
Seite
153-161
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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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1970-01-01T00:00:00Z