#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. We use $\mathbf{F} \text{ to denote } \mathbb{C} \text{ or } \mathbb{R},$ both of which are fields whose elements are scalars.