Tuples

$(a_1,a_2,\dots ,a_n)\text{ where }{a}_i\in F$ is an n-tuple (or list) with entries from F

Properties

• Two n-tuples are equal if elements for each index are equal
• Set of all n-tuples with entries from F is denoted $F^n$
  • $F^n$ is a vector space with coordinate-wise addition and scalar multiplication

Notation

Can be notated as either a column or a row

$$\begin{array}{r}\left(\begin{array}{c}{a}_1\\ a_2\\ ⋮\\ a_m\end{array}\right)\text{ or }(a_1,a_2,\dots ,a_n)\end{array}$$

Note: $F^3$ is 3D Vectors