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


    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
    StatePublished - May 1 2017



    • 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

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