3.5. Linear Transformations

Definition

Let \(V\) and \(W\) be vector spaces over the field \(F\). A linear transformation from \(V\) into \(W\) is a function \(T\) from \(V\) into \(W\) such that

\[T(c\alpha + \beta) = c(T(\alpha) + T\beta \quad \forall \alpha, \beta \in V, \forall c \in F\]