3.2. Hitch hiker’s guide

3.2.1. Defining a vector space

• Choose the field F over which vector space will be defined.

• Choose the set of objects V which will become vector space.

• Define the addition operation s.t.

  • Set is closed under addition

  • Commutativity holds

  • Associativity holds

  • Additive identity exists

  • Additive inverse exists

• Define the scalar multiplication (from a constant \(c \in F\)) s.t.

  • Scalar multiplication with 1 leads to no change

  • Distributive laws hold

  • Associative law holds over two multiplicands \(c_1, c_2\)

• Be Happy!