ABSTRACT
A variety of problems involving vector spaces and linear operators can only be addressed if we can measure the distance between vectors. For example, if we want to say that y is a good approximation to x, then we need a quantitative measure of the error y−x. As another example, when a system Ax = b has no solution, we might want to compute the x that makes Ax as close as possible to b. This also requires that we can measure the distance between vectors.
