A well kept secret of linear algebra is that having an inner product at all isn't as self-evident as it might seem. Euclidean distance might seem like some cano

A well kept secret of linear algebra is that having an inner product at all isn't as self-evident as it might seem. Euclidean distance might seem like some canonical notion of distance, but it doesn't have to be meaningful, especially if the choice of coordinates has no geometrical meaning.