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  • Matrices
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  • Basic terminology and notation
  • Operations on matrices
  • Particular types of matrices
  • Matrix equivalence
  • Canonical forms of matrices
  • Factorization of matrices
  • Similarity of matrices
  • Nonsingular matrices and equivalences
  • Eigenvalues and eigenvectors
  • Applications of band matrices
  • Determinants
  • Applications to cubic spline
  • Choosing factorizations and understanding numerical error
  • Rank and nullity
  • Applications to differential equations
  • Applications to Markov chains
  • Applications to error-correcting code
  • Application Leontief input-output analysis
  • Applications to voting and social choice
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  1. Choosing factorizations and understanding numerical error

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