The uniform normal form of a linear mapping

Richard Cushman

RECORD

The uniform normal form of a linear mapping

Richard Cushman

Symplectic Geometry · Submitted 27 May 2014

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

The authors' main claim This paper gives a normal form for $A$, which gives a better description of the structure of $A$ than the companion matrix.

how it is stated · asserted 1.00 read the record →

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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, 3,488 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Let $V$ be a finite dimensional vector space over a field $\mathrm{k}$ of characteristic $0$. Let $A$ be a linear mapping of $V$ into itself. This paper gives a normal form for $A$, which gives a better description of the structure of $A$ than the companion matrix. The computation of this normal form uses only operations from $\mathrm{k}$ and does not require finding roots of any polynomial.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Let $V$ be a finite dimensional vector space over a field $\mathrm{k}$ of characteristic $0$.	background 1.00	0.06	0.02	asserted 0.82
s1	Let $A$ be a linear mapping of $V$ into itself.	background 1.00	0.11	0.02	asserted 0.73
s2	This paper gives a normal form for $A$, which gives a better description of the structure of $A$ than the companion matrix.	contribution 0.92	0.93	0.86	asserted 1.00
s3	The computation of this normal form uses only operations from $\mathrm{k}$ and does not require finding roots of any polynomial.	method 0.95	0.85	0.12	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.71 · 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

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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

Let $V$ be a finite dimensional vector space over a field $\mathrm{k}$ of characteristic $0$. Let $A$ be a linear mapping of $V$ into itself. This paper gives a normal form for $A$, which gives a better description of the structure of $A$ than the companion matrix. The computation of this normal form uses only operations from $\mathrm{k}$ and does not require finding roots of any polynomial.

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