1 Chapter 6 projection

• dot-product : unitless magnitude of projection \((x \cdot w)\)
• direction: \(\frac{w}{w \cdot w}\)

\[Proj_w(x) = (x \cdot w) \frac{w}{w \cdot w}\]

• \(Proj_w(x)\) is a linear combination
  • \(cProj_w(x) = Proj_w(cx)\)
  • \(Proj_w(x_1 + x_2) = Proj_w(x_1) + Proj_w(x_2)\)

2 Chapter 7 Linear regression

3 Chapter 8 Multivariable functions

• scalar-valued function \(\mathbb{R}^n \rightarrow \mathbb{R}^1\)
  vector-valued function \(\mathbb{R}^n \rightarrow \mathbb{R}^m\)
  
• scalar-valued function means 1-DIM OUTPUT
  vector-valued function means multi-DIM OUTPUT