Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Gauche perspective on row reduced echelon form and its uniqueness   Using a left-to-right "sweeping" algorithm, we define the \emph{Gauche basis}
for the column space of a matrix $M$. By means of the Gauche basis we interpret
the row reduced echelon form of $M$, and give a direct proof of its uniqueness.
We conclude with pedagogical reflections.

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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph