Having established the role of linear algebra in machine learning and familiarized ourselves with the NumPy library, we now turn our attention to vectors. Vectors serve as fundamental objects for representing data points or features.

This chapter introduces the concept of a vector from both geometric and algebraic perspectives. We will cover standard mathematical notation for vectors and demonstrate how to represent them using NumPy arrays in Python. You will learn to perform essential vector operations, including:

• Addition and subtraction
• Scalar multiplication
• Calculating vector length using norms (like the $L_1$ and $L_2$ norms)
• Computing the dot product between two vectors

Practical examples using NumPy will accompany the mathematical definitions, ensuring you can apply these concepts directly in code. By the end of this chapter, you will be comfortable defining vectors and manipulating them using key operations.