Linear Algebra

Vector Space

Vector space is a set of “vectors” with a notion of Addition such that:

  • V is closed under addition
  • V is commutative
  • V is associative
  • For every A there is a zero vector such that [V+0=V]
  • For all Vectors in V there is a -V such that (-V)+V=0

And of a Scalar Multiplication such that:

  • V is closed under Scalar Multiplication
  • For All r,s are a set of real numbers and V is a Vector then (r+s)V= rV+sV
  • r is a set of real numbers and V, W are vectors, r(V+W)= rV+rW
  • r,s are a set of real numbers and V is a vector, (rs)V=r(sV)
  • 1*V=V

Book

Proofs:

  • Two vector after adding are still a vector, the commute a because they have same number of column array.
  • The order of adding the vectors doesn’t affect the result
  • (V+W)+U=V+(W+U) the parenthesis doesn’t affect the result
  • p1
  • p2
  • p3
  • p4
  • p5
  • p6
  • p7

 

 

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