BLOCK III. Vectors and linear combinations

Often, quantities are made out of multiple components. For example, the location of an object in space has $x$, $y$, and $z$ components. An important mathematical strategy for working with multiple components relates to the ideas of a vector and combinations of vectors as well as a set of vectors involved in a combination. (The set of vectors is called a matrix.)

Vectors appear naturally in physics: position, velocity, acceleration. They are also a principal building block of algorithms for machine learning, data science, and statistical modeling.

This Block introduces the basics of vectors and operations on vectors. There is a broad mathematical subject called “linear algebra” of which vectors and matrices are a part. Here, we focus on a compact set of ideas that are of particular importance in modeling and statistics.