Orthosymplectic diagonalization in Williamson's theorem

2024/03/18 by Hemant K. Mishra, Mishra, Hemant K.
Mathematics · Physics and Astronomy · #15A18 #15B48 #Advanced Mathematical Theories and Applications #Advanced Optimization Algorithms Research #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Mathematics and Applications #Quantum Physics (quant-ph) #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2403.11609

openalex publication_date 2024/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we provide an algebraic condition on any 2n × 2n real symmetric positive definite matrix which is necessary and sufficient for the matrix to be diagonalized by an orthosymplectic matrix in the sense of Williamson's theorem.

Related

• On Simultaneous Symplectic Diagonalization in the sense of Williamson's Theorem
• On generalization of Williamson's theorem to real symmetric matrices
• A New Form of Williamson's Product Theorem
• Simultaneous symplectic reduction of quadratic forms into normal forms
• Perturbation Bounds for Williamson's Symplectic Normal Form