This chapter introduces matrices, extending the concept of vectors to handle collections of data. A matrix, essentially a grid of numbers, serves two primary functions in machine learning: organizing datasets and performing geometric transformations.

We will cover fundamental matrix operations, including addition, subtraction, transposition, and multiplication. You'll learn how multiplying a vector by a matrix can represent linear transformations like scaling and rotation on data points. We will also examine different types of matrices (like identity and diagonal matrices) and see how they provide a compact way to represent systems of linear equations, often written in the form $Ax = b$.

Throughout the chapter, we'll implement these operations efficiently using the NumPy library in Python, preparing you to apply these concepts to practical machine learning tasks.