Total positivity of sums, Hadamard products and Hadamard powers: Results and counterexamples

Shaun Fallat, Charles R. Johnson, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We show that, for Hankel matrices, total nonnegativity (resp. total positivity) of order r is preserved by sum, Hadamard product, and Hadamard power with real exponent t≥r−2. We give examples to show that our results are sharp relative to matrix size and structure (general, symmetric or Hankel). Some of these examples also resolve the Hadamard critical-exponent problem for totally positive and totally nonnegative matrices.

    Original languageEnglish (US)
    Pages (from-to)242-259
    Number of pages18
    JournalLinear Algebra and Its Applications
    Volume520
    DOIs
    StatePublished - May 1 2017

    Fingerprint

    Totally Nonnegative Matrices
    Total Positivity
    Hadamard Product
    Hankel Matrix
    Hankel
    Nonnegativity
    Critical Exponents
    Counterexample
    Resolve
    Exponent

    Keywords

    • Hadamard critical exponent
    • Hadamard power
    • Hadamard product
    • Hankel matrix
    • Stieltjes moment problem
    • Totally nonnegative matrix
    • Totally positive matrix

    ASJC Scopus subject areas

    • Algebra and Number Theory
    • Numerical Analysis
    • Geometry and Topology
    • Discrete Mathematics and Combinatorics

    Cite this

    Total positivity of sums, Hadamard products and Hadamard powers : Results and counterexamples. / Fallat, Shaun; Johnson, Charles R.; Sokal, Alan D.

    In: Linear Algebra and Its Applications, Vol. 520, 01.05.2017, p. 242-259.

    Research output: Contribution to journalArticle

    Fallat, Shaun ; Johnson, Charles R. ; Sokal, Alan D. / Total positivity of sums, Hadamard products and Hadamard powers : Results and counterexamples. In: Linear Algebra and Its Applications. 2017 ; Vol. 520. pp. 242-259.
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