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Lower Bounds for the Smallest Singular Value of Certain Toeplitz-like Triangular Matrices with Linearly Increasing Diagonal Entries
Publikationstyp
Journal Article
Date Issued
2019-10
Sprache
English
Author(s)
Institut
TORE-URI
Volume
91
Issue
5
Article Number
39
Citation
Integral Equations and Operator Theory 5 (91) : 39 (2019-10)
Publisher DOI
Scopus ID
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.
Subjects
Frobenius norm
Infinite-dimensional matrix
Minimum singular value
Toeplitz-like triangular matrices