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  • Multiplication by a change of coordinates matrix converts representations for different bases.
  • Change of coordinates matrices are invertible
  • Definition of coordinates relative to a given basis
  • Basis exchange using a nonzero coordinate
  • Definition of coordinate vector/mapping/representation relative to a given basis
  • The coordinate vector relative to a given basis is a linear mapping to R^n (or C^n).
  • The coordinate vector relative to a given basis is an injective linear mapping to R^n (or C^n).
  • The coordinate vector relative to a given basis is a surjective linear mapping to R^n (or C^n).
  • Definition of change of coordinates matrix between two bases
  • The change of coordinates matrix between two bases exists and is unique
  • Conjugating by a change of coordinates matrix converts matrix representations with respect to different bases.
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  1. Change of coordinates matrices are invertible

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  • The change of coordinates matrix between two bases exists and is uniqueClose match
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