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  1. Chollet's inequality for positive semidefinite matrices of rank at most fourScott SchubrEdition 4 · 2026-11-02 Public
  2. Strong Self-Permanent Inequalities for Complex Four-Row Bipartite SupportsScott SchubrEdition 3 · 2026-10-28 Public
  3. Sharp trace-degree certificates for rank-two permanent-derivative compensationScott SchubrEdition 2 · 2026-10-27 Public
  4. A quantitative Chollet inequality for rank-four matrices of order sevenScott SchubrEdition 2 · 2026-10-27 Public
  5. Trace-perturbed minimizers of the mixed discriminantScott SchubrEdition 2 · 2026-10-27 Public
  6. Strong permanent inequalities for cycles and a class of single-chord supportsScott SchubrEdition 2 · 2026-10-27 Public
  7. Sharp limitations of two permanental cofactor comparisonsScott SchubrEdition 2 · 2026-10-27 Public
  8. Strong permanent inequalities on three chorded seven-cycle supportsScott SchubrEdition 2 · 2026-10-27 Public
  9. Coupled permanent cofactors: sharp occupation bounds and compensation geometryScott SchubrEdition 11 · 2026-10-27 Public
  10. Strong permanent inequalities for three-row bipartite supports and triangle-free supports through order sevenScott SchubrEdition 2 · 2026-10-27 Public
  11. Strong permanent contraction on four-row bipartite supports through six columnsScott SchubrEdition 2 · 2026-10-27 Public
  12. Strong permanent contraction on four-by-seven bipartite supportsScott SchubrEdition 2 · 2026-10-27 Public
  13. Finite-order positivity and growing negative inertia for averaged Riemann theta productsScott SchubrEdition 2 · 2026-10-27 Public
  14. Row-dependent bounds for strong permanent contraction on four-by-eight supportsScott SchubrEdition 2 · 2026-10-27 Public
  15. Sharp permanent-derivative compensation on the flat equal-spectrum conjugate-disjoint Gram stratumScott SchubrEdition 2 · 2026-10-27 Public
  16. Variance cancellation and two-direction bounds for six-row permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  17. Real-section permanent-derivative compensation and quadratic phase controlScott SchubrEdition 2 · 2026-10-27 Public
  18. Full-phase permanent-derivative compensation under real-part spectral pinchingScott SchubrEdition 2 · 2026-10-27 Public
  19. Phase-boundary reduction and low-rank compensation for permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  20. Asymptotically optimal bounds for permanental cofactor matricesScott SchubrEdition 2 · 2026-10-27 Public
  21. Uniform permanent-derivative compensation on the six-row conjugate-disjoint Gram locusScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 4

Chollet's inequality for positive semidefinite matrices of rank at most four

Scott Schubr

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Abstract

We prove Chollet's inequality in every matrix order for pairs of complex Hermitian positive semidefinite matrices when both factors have rank at most four. A controlled-loss extension of the occupation-border comparison of Li, Zhao and Luo propagates the strict reserve in an established singular-five bound with factor 3/5. We optimize the scalar balancing parameter, sharpen the resulting factors in orders seven through nine, and obtain an exact factor below 0.959 in order ten. The all-order conclusion combines this continuation with Rodtes' order-four theorem and Ma's large-order theorem. We include the complete interpretation and positivity proof of the inherited principal-minor sum-of-squares certificate, together with its unchanged data and standalone verifier. The coefficient-one inequality is strict for positive diagonal in orders at least five. The certificate and quantitative base are prior inputs; the continuation optimizes two explicitly defined coefficientwise losses.

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