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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
  • Determinants
  • Choosing factorizations and understanding numerical error
  • Rank and nullity

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  • Definition of singular value decomposition (SVD)
  • LU decomposition
  • Definition of rank factorization of a matrix
  • Definition of Cholesky decomposition
  • QR decomposition
  • Definition of Schur triangulation
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  1. Factorization of matrices

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