Associated Matrix of Operated Transformations

Topics: Algebra - Linear Transformation

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Let $V,W$ be vector spaces on $\mathbb{K}$, and let:

• $T:V\to W$, $S:V\to W$ be linear transformations
• $\beta$ be a basis for $V$, $\gamma$ be a basis for $W$

The associated matrices of $T$ and $S$, relative to addition and scalar multiplication, are given by:

$$[S+T{]}_{\beta }^{\gamma }=[S{]}_{\beta }^{\gamma }+[T{]}_{\beta }^{\gamma }$$

$$[\lambda T{]}_{\beta }^{\gamma }=\lambda [T{]}_{\beta }^{\gamma }$$