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Matrix methods: basic classical theory

2000· book-chapter· en· W4388321131 on OpenAlexaff
Johann Boos, Peter Cass

Bibliographic record

Venuenot available
Typebook-chapter
Languageen
FieldComputer Science
TopicMatrix Theory and Algorithms
Canadian institutionsWestern University
Fundersnot available
KeywordsConvergence (economics)Consistency (knowledge bases)Matrix (chemical analysis)Section (typography)Calculus (dental)MathematicsComputer scienceAlgebra over a fieldApplied mathematicsPure mathematicsDiscrete mathematics

Abstract

fetched live from OpenAlex

Abstract As we have already mentioned, in this and the following chapters we will deal mainly with matrix methods, in particular with their domains and the notion of convergence generated by them. Corresponding to the questions formulated in Section 1.3 we aim in Chapter 2 to give the most basic inclusion, comparison and consistency theorems. We will make use exclusively of classical (analytical) methods; some of these results we will re-prove in Parts II and III by functional analytic methods.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.003
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: none
Teacher disagreement score0.009
Threshold uncertainty score0.031

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.003
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0010.001
Science and technology studies0.0010.003
Scholarly communication0.0020.003
Open science0.0010.001
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0090.003

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.020
GPT teacher head0.296
Teacher spread0.276 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designNot applicable
Domainnot available
GenreOther

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations0
Published2000
Admission routes1
Has abstractyes

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