Linear Transformation Addition

Topics: Algebra - Linear Transformation

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

We define addition between $T$ and $S$ as:

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

…where $T+S:V\to W$.

$(T+S)(x)$ is linear.