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arXiv · 1201.2950

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

Alexandros G. Paraskevopoulos
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Abstract

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

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Alexandros G. Paraskevopoulos. 2012-01-13. The Infinite Gauss-Jordan Elimination on Row-Finite ω x ω Matrices. https://arxiv.org/abs/1201.2950

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