Two Forms of the Dot Product

the goal of PCA is to find new dimensions – which are a combination of the original dimensions the same way intelligence could be a combination of cleverness and quick-wittedness – that capture as much of the variance in the data as possible.

the mathematical secret behind finding curves of minimum length, or any other property.

realized that there were two radically different ways of looking at the instruction we were receiving, and that the two approaches were mutually incompatible. The first approach consists of treating mathematics as knowledge. Mathematical statements are information that you have to ingest and be able to recall. You have to learn the definitions, lea

In ordinary Euclidean space, the dot product of two vectors is the product of the length of both vectors times the cosine of the angle between them.