Examples of Linear Transformations

[!Theorem 5.2.1]

Let $\vec{d}\in {\mathbb{R}}^n$ with $\vec{d}\ne \vec{0}$

• The function $T:{\mathbb{R}}^n\to {\mathbb{R}}^n$ defined by $T(\vec{x})=pro{j}_{\vec{d}}\vec{x}$ is linear
• The function $S:{\mathbb{R}}^n\to {\mathbb{R}}^n$ defined by $S(\vec{x})=per{p}_{\vec{d}}\vec{x}$ is linear