Set of Linear Transformations

Notation

• Let $V,W$ be vector spaces
• Define $\mathcal{L}(V,W)$ to be the set of all Linear Maps $T:V\to W$
• $\mathcal{L}(V)$ denotes a Set of Linear Operators $T:V\to V$

Properties

• $L(V,W)$ is a Vector Space

Dimension

• With $dim(V)=n<\infty$
• With $dim(W)=m<\infty$
• $dim(\mathcal{L}(V,W))=nm$ Dimension of Set of Linear Transformations Theorem

Concepts

• Set of Linear Transformations is a Vector Space Theorem
• Size of Set of Linear Transformations Theorem
• Set of Linear Operators
• Linear Operator
• Dimension of Set of Linear Transformations Theorem