Field

• Set on which addition and multiplication defined
  • Behave same as on rational and real numbers
  • Subtraction, division implied
• Examples
  • Rational numbers
  • Real numbers
  • Complex numbers
• Any field can be used as scalars for a vector space
• A commutative ring where 0 =/= 1 and all nonzero elements are invertible

Vector Space

• Set of vectors
  • Can be added together and multiplied by scalar
    • Can be scaled by complex numbers
      • Part of definitions
    • Must satisfy vector axioms