How Many Eigenvalues of a Random Symmetric Tensor are Real?

2017/01/25 by Paul Breiding, Breiding, Paul
Mathematics · Medicine · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Advanced Neuroimaging Techniques and Applications #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1701.07312

openalex publication_date 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article answers a question posed by Draisma and Horobet, who asked for a closed formula for the expected number of real eigenvalues of a random real symmetric tensor drawn from the Gaussian distribution relative to the Bombieri norm. This expected value is equal to the expected number of real critical points on the unit sphere of a Kostlan polynomial. We also derive an exact formula for the expected absolute value of the determinant of a matrix from the Gaussian Orthogonal Ensemble.

Citations

• Tensor Decompositions and Applications

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