Linear Transformation Scalar Multiplication

Topics: Algebra - Linear Transformation

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Let $V,W$ be vector spaces on $\mathbb{K}$ with a finite dimension, $T:V\to W$ a linear transformation and $\lambda \in \mathbb{K}$.

We define the scalar multiplication of $\lambda$ by $T$ as:

$$(\lambda T)(x):=\lambda T(x),\forall x\in V,\lambda \in \mathbb{K}$$

…where $\lambda T:V\to W$.

$\lambda T$ is linear.