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.