Metadata
Mathematics Graduate Analyze Medium
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Metadata

  • Subject

    Mathematics

  • Education level

    Graduate

  • Cognitive goals

    Analyze

  • Difficulty estimate

    Medium

  • Tags

    eigenvalues, eigenvectors, conditioning, perturbation theory, numerical linear algebra, matrix analysis

  • Number of questions

    5

  • Created on

  • Generation source

    Fully autonomous and synthetic. Generation by GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • Prompt

    Assess graduate students' ability to analyze sensitivity of eigenvalues and eigenvectors to matrix perturbations: compute eigenvalue and eigenvector condition numbers, apply Bauer-Fike and Davis-Kahan (sin theta) bounds, derive first-order perturbation formulas, interpret pseudospectra, compare normal vs nonnormal behavior, and evaluate error bounds for simple, clustered, and multiple eigenvalues through short proofs and numerical examples.
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Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.