Linear Algebra

Linear algebra is the study of linear transformations on finite-dimensional vector spaces. While that might sound a bit intimidating at first, we’ll build our understanding completely from the ground up—so there’s no need to worry. We’ll start with vector spaces as our foundation and gradually introduce new ideas—each one acting like an upgrade that helps us tackle more complex problems.

From a mathematical perspective, linear algebra has countless applications, largely because its ideas are abstract and highly general. Throughout, I’ll present these abstract definitions but explain the underlying concepts using concrete examples—such as lists of numbers and geometric interpretations with arrows in space—to build strong intuition. We’ll focus on lists of numbers in particular, since that representation is most common in machine learning.

So, what exactly are vector spaces?