Definition:Set of All Linear Transformations/Vector Space

Definition

Let $K$ be a field.

Let $X, Y$ be vector spaces over $K$.

Then $\map {\LL} {X, Y}$ is the set of all linear transformations from $X$ to $Y$:

$\map {\LL} {X, Y} := \set {\phi: X \to Y: \phi \mbox{ is a linear transformation} }$

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 2.1$: Continuous and linear maps. Linear transformations