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The Number of Eigenvalues of a Tensor

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arxiv 1004.4953 v2 pith:ZHCTSSOA submitted 2010-04-28 math.NA cs.NAmath.AG

Dustin Cartwright , Bernd Sturmfels This is my paper · ORCID
classification math.NAcs.NAmath.AG
keywords eigenvaluesnumbertensoreigenvectorsalgebraalwayscharacteristiccoefficients
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Eigenvectors of tensors, as studied recently in numerical multilinear algebra, correspond to fixed points of self-maps of a projective space. We determine the number of eigenvectors and eigenvalues of a generic tensor, and we show that the number of normalized eigenvalues of a symmetric tensor is always finite. We also examine the characteristic polynomial and how its coefficients are related to discriminants and resultants.

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  1. Quantum estimates for classical polynomial optimization

    math-ph 2026-07 conditional novelty 5.0 of 10

    A quantum-variational matrix method is proposed for bounding homogeneous polynomials, with converging numerical tensor-eigenvalue estimates and a new conjectured inequality for Biasi's resonant Hamiltonians.

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