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Entropy and Hadamard Matrices

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H. Gopalkrishna Gadiyar, K.M. Sangeeta Maini, R. Padma, H.S. Sharatchandra

Mathematical Physics · Submitted 13 Jun 2002

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

The authors' main claim It provides a new interpretation of Hadamard matrices as those that saturate the bound for entropy.It appears to be a useful Morse function on the group manifold.

how it is stated · asserted 0.62 read the record →

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arXiv IDmath-ph/0206018 (version 2)
Pith IDHSR4V2Y2, Pith's permanent record of this paper and its review
CitationH. Gopalkrishna Gadiyar, H.S. Sharatchandra, K.M. Sangeeta Maini, R. Padma. "Entropy and Hadamard Matrices." arXiv:math-ph/0206018 (2002). https://pith.science/paper/HSR4V2Y2
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,039 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.13 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.09 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The entropy of an orthogonal matrix is defined. It provides a new interpretation of Hadamard matrices as those that saturate the bound for entropy.It appears to be a useful Morse function on the group manifold. It has sharp maxima and other saddle points. The matrices corresponding to the maxima for 3 and 5 dimensions are presented. They are integer matrices (upto a rescaling).

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 entropy of an orthogonal matrix is defined. contribution 0.89 0.69 0.07 asserted 1.00
s1 It provides a new interpretation of Hadamard matrices as those that saturate the bound for entropy.It appears to be a useful Morse function on the group manifold. interpretation 0.90 0.77 0.66 asserted 0.62
s2 It has sharp maxima and other saddle points. result 0.96 0.73 0.07 asserted 1.00
s3 The matrices corresponding to the maxima for 3 and 5 dimensions are presented. result 0.71 0.86 0.09 asserted 1.00
s4 They are integer matrices (upto a rescaling). result 1.00 0.82 0.08 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.94 · evidence from proof or derivation 0.72.

What was examined, and what was not

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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 entropy of an orthogonal matrix is defined. It provides a new interpretation of Hadamard matrices as those that saturate the bound for entropy.It appears to be a useful Morse function on the group manifold. It has sharp maxima and other saddle points. The matrices corresponding to the maxima for 3 and 5 dimensions are presented. They are integer matrices (upto a rescaling).

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