#math/linear-algebra #flashcards/math A Field is a set containing at least two distinct elements, 0 and 1, has the operations of addition and multiplication, and satisfies the following six properties: Commutativity, Associativity, (add/multiply) Identities, Additive Inverse, Multiplicative Inverse, Distributive. The book utilizes $F \text{ to denote } \mathbb{C} \text{ or } \mathbb{R}.$ Elements of $F$ are called _scalars_ (a number), as opposed to a vector. ## F${}^n$ $F^n$ is the set of all _lists_ of length $n$ of elements of $F$. Formally defined: $ F^n = \{(x_{1}, \dots, x_{n}) : x_{i} \in{} F \text{ for } i = 1, \dots, n \} $ ## List A _list_ of length $n$, where $n \in{} \mathbb{N} \cup \{0\}$, is an _ordered_ collection of $n$ elements (numbers, other lists or other abstract entities). $ (x_{1}, \dots, x_{n}) $