Arithmetical Structure

<p>Arithmetic with vectors:

One-dimensional (λ being a scalar):

(a) + (b) ≡ (a + b)

(a) - (b) ≡ (a - b)

λ(a) ≡ (λa)

Two-dimensional:

(a,b) + (c,d) ≡ (a + c, b + d)    (addition)

(a,b) - (c,d) ≡ (a - c, b - d)        (subtraction)

λ(a,b) ≡ (λa, λb)                    (scalar multiplication)

Note that multiplication of vecors is not defined at this stage.

Also the addition and subtraction of vectors is simplified if they are translated to begin or start at the same point.</p>