2.1: Orthogonal vectors and subspaces
Vectors are easier to understand when they're
described in terms of orthogonal bases. In addition, many of the
spaces we're interested in are orthogonal to each other.
If A is a rectangular matrix, Ax = b is often unsolvable. The matrix
ATA will help us find a vector x̂ that comes as close as possible
to solving Ax = b.