Linear Transformation Composition

Topics: Algebra - Linear Transformation

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Let $U,V,W$ be vector spaces on $\mathbb{K}$. Let $S:U\to V$ and $T:V\to W$ be linear transformations.

We define the composition of $T$ and $S$, denoted $T\circ S$, as:

$$(T\circ S)(x)=T(S(x)),\forall x\in V$$

…where $T\circ S:U\to W$ and is linear.