Let L be a lower triangular n× n-Toeplitz matrix with first column (μ, α, β, α, β, … ) T, where μ, α, β≥ 0 fulfill α- β∈ [ 0 , 1 ) and α∈ [ 1 , μ+ 3 ]. Furthermore let D be the diagonal matrix with diagonal entries 1 , 2 , … , n. We prove that the smallest singular value of the matrix A: = L+ D is bounded from below by a constant ω= ω(μ, α, β) > 0 which is independent of the dimension n.
