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On the Matrix With Elements 1/(r+s-1)

Published online by Cambridge University Press:  20 November 2018

W. W. Sawyer
W. W. Sawyer*
Affiliation:
Department of Mathematics and Faculty of Education, University of Toronto
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A standard example of a matrix for which the computation of eigenvectors and eigenvalues is very awkward is the matrix A with ars=1/(r+s—1), 1≤r≤n, 1 ≤s≤n. It is therefore of interest that A commutes with a tridiagonal matrix.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 2 , 01 June 1974 , pp. 297 - 298
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Gantmacher, F. R. and Krein, M. G.. Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Syst?me. Akademie-Verlag, Berlin, 1960.Google Scholar
2. Sawyer, W. W., Journal of the London Mathematical Society, 34 (1959), 451-453.Google Scholar