1987/04/01 by Dipa Choudhury, Roger A. Horn · 2 citations
Computer Science · Engineering · Mathematics · #Matrix Theory and Algorithms #graph theory and CDMA systems #Advanced Topics in Algebra #Mathematics #Invertible matrix #Polar decomposition #Hermitian matrix #Factorization #Unitary state #Pure mathematics #Square (algebra) #Triple system #Square matrix #Combinatorics #Symmetric matrix #Polar #Algebra over a field #Algorithm #Geometry
paper · doi:10.1137/0608019
openalex publication_date 1987/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
Every square complex matrix A can be factorized as A = UH, where U is unitary and H is positive semi-definite Hermitian. If A is nonsingular, it is known that one may write A = QS, where Q is complex orthogonal and S is complex symmetric. We develop necessary and sufficient conditions for there to be a factorization of this type when A is singular, and we give sufficient conditions for there to be at least one such factorization in which the factors commute.