Projection

• We can use the dot product and 2-norm to project a vector onto another.
• Projection of $y$ unto $x$
  • Signed scalar projection: $x^{T}y/\Vert x{\Vert }_2$
  • Vector projection:

$$\frac{x^{T}y}{\Vert x{\Vert }_2^2}x$$

• If $x$ is a unit vector ($\Vert x{\Vert }_2=1$), we simply have that the projection is equal to to $x^{T}y$ and $(x^{T}y)x$ for the vector expression.

Dot product, Vector norms