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XVI.—Some Continuant Determinants arising in Physics and Chemistry—II*

Published online by Cambridge University Press:  14 February 2012

D. E. Rutherford
D. E. Rutherford
Affiliation:
United College, University of St. Andrews
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Synopsis

Some of the formulae obtained in this paper are likely to find application in problems concerning a rectangular lattice of “atoms”, each of which is under the influence of its near neighbours. Some of the determinants considered apply to cases in which both the nearest and the next nearest neighbours are operative. The inverses of certain types of matrices are found, and these may prove to be of value either in solving systems of linear equations such as arise in relaxation problems, or in determining the latent roots of matrices which may occur in problems in applied mathematics.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 63 , Issue 3 , 1952 , pp. 232 - 241
Copyright
Copyright © Royal Society of Edinburgh 1952

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References

REFERENCES TO LITERATURE

Duncan, W. J., 1960. “Dependence of Errors in the Natural Frequencies of the Numbers of Elements in a Segmental Representation of a Uniform Shaft”, College of Aeronautics, Granfield. Report.Google Scholar
MacDuffee, C. C., 1933. The Theory of Matrices, Berlin.CrossRefGoogle Scholar
Rutherford, D. E., 1947. “Some Continuant Determinants Arising in Physics and Chemistry”, Proc. Roy. Soc. Edin., A, LXII, 229–236.Google Scholar
Stephanos, C., 1900. “Sur une extension du calcul des substitutions linéaires”, Journ. de Mathématiques, V, vi, 73–128.Google Scholar
Todd, John, 1960. “The Condition of a Certain Matrix”, Proc. Gamb. Phil. Soc, XLVI, 116–118.Google Scholar