1 Intuition
All of the valid outputs of the function, everything that the function can equal when fed an element of the domain.
2 In the context of linear algebra (Axler 3.18)
For \(T\) a function from \(V\) to \(W\), the range of \(T\) is the subset of \(W\) consisting of those vectors that are of the form \(Tv\) for some \(v \in V\): \[\text{range }T = \{Tv : v \in V\}\]
2.1 #aka image aka
2.2 #aka column space
The span of the columns