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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
  • Rank and mullity
  • Eigenvalues and eigenvectors
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  • Definition of similar matrices
  • Similarity of matrices in an equivalence relation.
  • Definition of similarity transform
  • Similar matrices have the same eigenvalues and the same characteristic polynomials.
  • Every square matrix is similar to one in Jordan form.
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