Working with vectors and matrices, the language of data.
Linear algebra is the bedrock of machine learning. At its core, it's the study of vectors, matrices, and the operations performed on them. In ML, data is almost always represented in these forms. A single data point, like a user's age, income, and spending score, can be represented as a vector. A whole dataset of many users is then represented as a matrix, where each row is a user (a vector) and each column is a feature. This structured representation is what allows computers to perform complex calculations on large datasets efficiently. Key concepts you'll need to master include vector and matrix addition, subtraction, and multiplication. One particularly important operation is the dot product, which is fundamental to how linear models and neural networks calculate weighted sums of inputs. You'll also learn about concepts like matrix transpose, inverse, and determinants, which are used in solving systems of linear equations and in algorithms like Principal Component Analysis (PCA). Understanding concepts like eigenvalues and eigenvectors is crucial for dimensionality reduction techniques, which help in simplifying complex datasets without losing significant information. Grasping linear algebra allows you to understand how an algorithm like linear regression is just solving a system of linear equations, or how a neural network is essentially a series of matrix multiplications and transformations. It's the language that lets us describe and manipulate data at scale.