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Record W1999708677 · doi:10.1112/jlms/jdn085

Super-identical pseudospectra

2009· article· en· W1999708677 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueJournal of the London Mathematical Society · 2009
Typearticle
Languageen
FieldComputer Science
TopicMatrix Theory and Algorithms
Canadian institutionsUniversité Laval
FundersUniversité Laval
KeywordsInteger (computer science)MathematicsInvariant (physics)CombinatoricsPure mathematicsComplex matrixMathematical physicsComputer scienceChemistry

Abstract

fetched live from OpenAlex

The complex N × N matrices A and B are said to have super-identical pseudospectra if, for each z ∈ ℂ, the singular values of A − zI are the same as those of B − zI. We explore this condition and its consequences. On the positive side, drawing on ideas from invariant theory, we prove that there exists an integer m = m(N) such that ‘almost every’ m-tuple of N × N matrices with super-identical pseudospectra contains a pair that are unitarily equivalent. On the negative side, we present an example of a pair of non-derogatory 4 × 4 matrices A and B with super-identical pseudospectra such that ||A2|| ≠ ||B2||.

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.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.677
Threshold uncertainty score0.290

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0020.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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 head0.009
GPT teacher head0.242
Teacher spread0.233 · 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