Orthogonal projections

This is one of those tutorials that bring many ideas we've been building together into something applicable. Orthogonal projections (which can sometimes be conceptualized as a "vector's shadow" on a subspace if the light source is above it) can be used in fields varying from computer graphics and statistics!If you're familiar with orthogonal complements, then you're ready for this tutorial!

Projections onto subspaces

Visualizing a projection onto a plane

A projection onto a subspace is a linear transformation

Subspace projection matrix example

Another example of a projection matrix

Projection is closest vector in subspace

Least squares approximation

Least squares examples

Another least squares example