The Expected Number of Eigenvalues of a Real Gaussian Tensor

DOI10.1137/16M1089769zbMath1365.65092arXiv1604.03910OpenAlexW2963202796MaRDI QIDQ5737777

Paul Breiding

Publication date: 30 May 2017

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.03910

zbMATH Keywords

eigenvalueseigenvalue distributionGaussian random variablesrandom polynomialscomputational algebraic geometrytensors

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Random matrices (algebraic aspects) (15B52) Multilinear algebra, tensor calculus (15A69)

Related Items (11)

A very brief introduction to nonnegative tensors from the geometric viewpoint ⋮ Newton Correction Methods for Computing Real Eigenpairs of Symmetric Tensors ⋮ Certifying the global optimality of quartic minimization over the sphere ⋮ Signed distributions of real tensor eigenvectors of Gaussian tensor model via a four-Fermi theory ⋮ Exact analytic expressions of real tensor eigenvalue distributions of Gaussian tensor model for small N ⋮ The Expected Number of Eigenvalues of a Real Gaussian Tensor ⋮ Probabilistic Schubert calculus ⋮ The real polynomial eigenvalue problem is well conditioned on the average ⋮ The Dynamics of Swamps in the Canonical Tensor Approximation Problem ⋮ How many eigenvalues of a random symmetric tensor are real? ⋮ Dual core generalized inverse of third-order dual tensor based on the T-product

Uses Software

• Maple
• Matlab
• Bertini

Cites Work

• Tensor Decompositions and Applications
• Distribution of the eigenvalues of a random system of homogeneous polynomials
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• Condition
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• The Z -eigenvalues of a symmetric tensor and its application to spectral hypergraph theory
• Low-Rank Approximation of Tensors
• The average number of critical rank-one approximations to a tensor
• Uniform Asymptotic Expansions of the Incomplete Gamma Functions and the Incomplete Beta Function
• How Many Eigenvalues of a Random Matrix are Real?
• COMPLEXITY AND REAL COMPUTATION: A MANIFESTO
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• The Best Rank-1 Approximation of a Symmetric Tensor and Related Spherical Optimization Problems
• The Expected Number of Eigenvalues of a Real Gaussian Tensor
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