Geodesic
On the Matrix With Elements 1/(r+s-1)
Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 297-298

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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. 
Sawyer, W. W. On the Matrix With Elements 1/(r+s-1). Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 297-298. doi: 10.4153/CMB-1974-059-0
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[1] 1. Gantmacher, F. R. and Krein, M. G.. Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Syst?me. Akademie-Verlag, Berlin, 1960. Google Scholar

[2] 2. Sawyer, W. W., Journal of the London Mathematical Society, 34 (1959), 451-453. Google Scholar

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