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Characterization of the class of canonical forms for systems of linear equations

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JC Ndogmo

Classical Analysis and ODEs · Submitted 25 Feb 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is then shown that the normal form of linear systems reducible by an invertible point transformation to the canonical equation $\by^{(n)}=0$ consists of copies of the same iterative equation.

how it is stated · asserted 1.00 read the record →

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arXiv ID1502.07164 (version 1)
Pith IDATBLTUXP, Pith's permanent record of this paper and its review
CitationJC Ndogmo. "Characterization of the class of canonical forms for systems of linear equations." arXiv:1502.07164 (2015). https://pith.science/paper/ATBLTUXP
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,934 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation to the canonical equation $\by^{(n)}=0$ consists of copies of the same iterative equation. Other properties of iterative linear systems are also derived, as well as the superposition formula for their general solution.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. result 0.54 0.85 0.21 asserted 1.00
s1 It is then shown that the normal form of linear systems reducible by an invertible point transformation to the canonical equation $\by^{(n)}=0$ consists of copies of the same iterative equation. result 0.98 0.90 0.42 asserted 1.00
s2 Other properties of iterative linear systems are also derived, as well as the superposition formula for their general solution. result 0.86 0.90 0.14 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation to the canonical equation $\by^{(n)}=0$ consists of copies of the same iterative equation. Other properties of iterative linear systems are also derived, as well as the superposition formula for their general solution.

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1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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