On the principal minors of Fourier matrices

2024/09/15 by Andrei Caragea, Caragea, Andrei, Dae Gwan Lee +1 · 2 citations
Computer Science · Mathematics · #11C20 #42A99 #42C15 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2409.09793

openalex publication_date 2024/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the N-dimensional Fourier matrix F_N, we prove that if N≥ 4 is square-free, then every 2 × 2 and 3× 3 principal minor of F_N is nonzero. We also show that if N≥ 4 is not square-free, then F_N has zero principal minors of all sizes. Moreover, based on numerical experiments, we conjecture that if N is square-free, then all principal minors of F_N are nonzero.

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