Linear Function

Description:

• It is a vector function that has function $f(x)=a^{T}x$
  • for $f:{\mathbb{R}}^n\to \mathbb{R}$ with $a\in {\mathbb{R}}^n$
• Vector $a$ can be viewed as a linear map

Affine function

• It is a vector function that has function $f(x)=a^{T}x+b$
  • for $f:{\mathbb{R}}^n\to \mathbb{R}$ with $a\in {\mathbb{R}}^n$ and $b\in \mathbb{B}$
  • and $a,b$ are independent
• We can obtain $a$ and $b$:
  • $a(i)=f(e_i)-b$ for $i=1,...n$
  • $b=f(0)$