Composition of linear transformations

Dependencies:

1. Linear transformation

Let $S: U \mapsto V$ and $T: V \mapsto W$ be linear transformations. Then $ST$ is a linear transformation from $U$ to $W$.

Proof

\[ (ST)(u_1 + u_2) = S(T(u_1 + u_2)) = S(T(u_1) + T(u_2)) = S(T(u_1)) + S(T(u_2)) = (ST)(u_1) + (ST)(u_2) \] \[ (ST)(cu) = S(T(cu)) = S(cT(u)) = cS(T(u)) = c(ST)(u) \]

Dependency for:

1. Canonical decomposition of a linear transformation
2. Vector space isomorphism is an equivalence relation

Info:

• Depth: 5
• Number of transitive dependencies: 5

Transitive dependencies:

1. Group
2. Ring
3. Field
4. Vector Space
5. Linear transformation