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Basis Vectors

• Basis of a coordinate system
  • What's scaled in the xy coordinate system
  • Everything is expressed in terms of these basis vectors
  • Set of linearly independent vectors that span the full space.
  • Can transform between basis vectors using matrix multiplication.
    • A^-1 M A = represent a transformation in another basis system.
    • Can raise A^n by using basis vectors
      • A^n = S (S^-1 A S)^n S^-1
  • [[3b1b essence]]

— Kunal