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  • Algebraic properties of R^n (or C^n)

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  • Definition of scalar
  • Definition of vector
  • Definition of column vector
  • Definition of R^n (or C^n)
  • Definition of size of a vector
  • Definition of entry/component of a vector
  • Definition of 0 vector
  • Definition of equality of vectors
  • Definition of vector sum/addition
  • Vector sum/addition is commutative and associative
  • Definition of conjugate of a vector in C^n
  • Definition of the real part of a vector in C^n
  • Definition of the imaginary part of a vector in C^n
  • The conjugate of a sum of vectors in C^n is the sum of the conjugates
  • Definition of vector-scalar multiplication
  • The conjugate of vector-scalar multiplication in C^n is the product of the conjugates.
  • Example of vector-scalar multiplication in R^2
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  1. Definition of entry/component of a vector

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