2025/01/21 by Arijit Mukherjee, Mukherjee, Arijit, Arindam Sutradhar +1
Computer Science · Engineering · Physics and Astronomy · #05C50 #11E25 #13D02 #14N25 #14P05 #90C90 #Advanced Mathematical Theories and Applications #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Optimization and Control (math.OC) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2501.12063
openalex publication_date 2025/01/21 · openalex created_date 2025/01/24 · openalex updated_date 2026/07/28
Given a positive noncommutative polynomial f, equivalently a sum of Hermitian squares (SOHS), there exists a positive semidefinite Gram matrix that encrypts all the structural essence of f. There are no available methods for extending a noncommutative polynomial to a SOHS keeping the Gram matrices unperturbed. As a remedy, we introduce an equally significant notion of Gram-like matrices and provide linear algebraic techniques to get the desired extensions. We further use positive semidefinite completion problem to get SOHS and provide criteria in terms of chordal graphs and 2-regular projective algebraic sets.