On a classic example in the nonnegative inverse eigenvalue problem
Thomas J. Laffey, Helena Šmigoc · Electronic Journal of Linear Algebra · 2008
This paper presents a construction of nonnegative matrices with nonzero spectrum τ = (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 τ to zero as a function of the number of zeros that are added to the spectrum.