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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
  • Determinants

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  • Definition of equivalent matrices
  • Equivalent matrices represent the same linear transformation with resect to appropriate bases.
  • A matrix of rank k is equivalent to a matrix with 1 in the first k diagonal entries and 0 elsewhere.
  • Two matrices of the same size are equivalent if and only if they have the same rank.
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