Geodesic
On a classic example in the nonnegative inverse eigenvalue problem
The electronic journal of linear algebra, Tome 17 (2008), pp. 333-342.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This paper presents a construction of nonnegative matrices with nonzero spectrum $\tau $= (3 + t, 3 - t, - 2, - 2, - 2) for t > 0. The result presented gives a constructive proof of a result of Boyle and Handelman in this special case. This example exhibits a surprisingly fast convergence of the spectral gap of $\tau $to zero as a function of the number of zeros that are added to the spectrum.
Classification : 15A48, 15A18, 15A29
Keywords: nonnegative matrices, nonnegative inverse eigenvalue problem, spectral gap, companion matrices 
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     title = {On a classic example in the nonnegative inverse eigenvalue problem},
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Laffey, Thomas J.; Šmigoc, Helena. On a classic example in the nonnegative inverse eigenvalue problem. The electronic journal of linear algebra, Tome 17 (2008), pp. 333-342. http://geodesic.mathdoc.fr/item/ELA_2008__17__a21/