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

Kelly Pearson and Tan Zhang ()
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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

Mathematics, 2024, vol. 12, issue 5, 1-18

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.

Keywords: tensor eigenvalues; higher order tensor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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