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  • Matrices as linear transformations

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  • Matrices act as a transformation by multiplying vectors
  • Matrix-vector multiplication is a linear transformation.
  • Definition of the standard matrix for a linear transformation
  • A linear transformation is given by a matrix whose columns are the images of the standard basis vectors
  • A linear transformation is given by a matrix with respect to a given basis.
  • Definition of nilpotent linear transformation
  • Definition of matrix representation of a linear transformation
  • Matrix representation of a composition of linear transformations is given by a matrix product
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  1. A linear transformation is given by a matrix whose columns are the images of the standard basis vectors

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