The Infinite Gauss-Jordan Elimination on Row-Finite ω x ω\ Matrices

Details The Infinite Gauss-Jordan Elimination on Row-Finite ω x ω\ Matrices The Infinite Gauss-Jordan Elimination on Row-Finite ω x ω\ Matrices

2012-01-13

arxiv.org/abs/1201.2950v1

Mathematics

Functional Analysis

35 pages

Scientific paper

The Gauss-Jordan elimination algorithm is extended to reduce a row-finite $\omega\times\omega$ 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 $\omega\times\omega$ matrix is fully constructible.

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