Linear Algebra for Data Science

Linear algebra is the mathematics of vectors and matrices. It is the language of data science and machine learning.

**Vectors:** As we've seen in physics, a vector is a list of numbers representing a point in space. In data science, a vector can represent a single data point with many features. For example, a user could be represented by a vector [age, income, screen_time].

**Matrices:** A matrix is a grid of numbers, or a collection of vectors. A whole dataset can be represented as a matrix, where each row is a data point (a user) and each column is a feature.

**Why is this useful?**
By representing data as vectors and matrices, we can use powerful linear algebra operations to manipulate it at scale. For example, multiplying matrices is a fundamental operation in neural networks. Libraries like NumPy in Python are highly optimized for these operations, allowing us to process massive datasets efficiently. Understanding the concepts of matrix multiplication, dot products, and transformations is key to understanding how many machine learning models work.