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The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given Point

Author

Listed:
  • Kelly Pearson

    (Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, USA)

  • Tan Zhang

    (Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, USA)

Abstract

We begin with a degree m real homogeneous polynomial in n indeterminants and bound the distance from a given n -dimensional real vector to the real vanishing of the homogeneous polynomial. We then apply these bounds to the real homogeneous polynomial associated with a nonzero m -order n -dimensional weakly symmetric tensor which has zero as an eigenvalue. We provide “nested spheres” conditions to bound the distance from a given n -dimensional real vector to the nearest zero eigenvector.

Suggested Citation

  • Kelly Pearson & Tan Zhang, 2024. "The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given Point," Mathematics, MDPI, vol. 12(5), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:705-:d:1347750
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    Keywords

    tensor eigenvalues; higher order tensor;

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