2012/01/13 by Alexandros G. Paraskevopoulos, Paraskevopoulos, Alexandros G.
Mathematics · #15A21 #16S50 #65F05 #FOS: Mathematics #Functional Analysis (math.FA) #Rings and Algebras (math.RA) #math.FA #math.RA #msc:15A21 #msc:16S50 #msc:65F05
paper · pdf · doi:10.48550/arxiv.1201.2950
35 pages
arxiv created 2012/01/13 · arxiv updated 2012/01/17
The Gauss-Jordan elimination algorithm is extended to reduce a row-finite ω×ω matrix to lower row-reduced form, founded on a strategy of rightmost pivot elements. Such reduced matrix form preserves row equivalence, unlike the dominant (upper) row-reduced form. This algorithm provides a constructive alternative to an earlier existence and uniqueness result for Quasi-Hermite forms based on the axiom of countable choice. As a consequence, the general solution of an infinite system of linear equations with a row-finite coefficient ω×ω matrix is fully constructible.