Determinants
The determinant compresses an entire square matrix into a single number that answers two questions at once: and It is less central to computation than students often think (we rarely compute large determinants), but its
阅读文章 →Vector Spaces and the Four Fundamental Subspaces
This is the conceptual heart of linear algebra. Everything so far — vectors, systems, matrices — now gets organized by a single powerful abstraction: the and its . The payoff is the , which describes the four subspaces h
阅读文章 →Linear Transformations and Change of Basis
We have treated matrices as arrays of numbers. This chapter elevates them to their true identity: matrices linear transformations once a basis is fixed. This view explains why matrix multiplication is defined the way it
阅读文章 →Orthogonality, Projections, and Least Squares
Orthogonality is where linear algebra becomes a tool for data. When an exact solution to = does not exist — the everyday situation with real, noisy, over-determined data — orthogonality tells us how to find the approxima
阅读文章 →Eigenvalues and Eigenvectors
Eigenvalues reveal the hidden axes of a transformation — the special directions a matrix merely stretches without rotating. They explain the long-term behavior of dynamical systems, the principal directions of data, the
阅读文章 →Symmetric Matrices, the Spectral Theorem, and Quadratic Forms
Symmetric matrices (=) are the best-behaved objects in linear algebra, and — not coincidentally — the ones that appear most in machine learning: covariance matrices, Gram matrices, kernel matrices, and Hessians are all s
阅读文章 →The Singular Value Decomposition
If one theorem deserves the title ``fundamental theorem of data science,'' it is the singular value decomposition. The SVD factors matrix — square or rectangular, full-rank or not — into a rotation, a scaling, and anothe
阅读文章 →Matrix Decompositions, Norms, and Numerical Linear Algebra
On a real computer, linear algebra is done in finite-precision arithmetic, where the order of operations and the conditioning of a problem decide how many correct digits survive. This chapter consolidates the major matri
阅读文章 →Tensors and Matrix Calculus
Two ideas carry linear algebra the last mile into deep learning. First, generalize vectors and matrices to higher-order arrays — the natural container for images, sequences, and batches. Second, extends derivatives to ve
阅读文章 →Linear Algebra in Machine Learning, Deep Learning, and AI
This final chapter is the payoff. Every concept in the book reappears here as the working machinery of modern AI. The thesis is simple and, by now, earned: Data are tensors; models are matrices; learning is optimization
阅读文章 →Preface: how to use this book
Linear algebra is the mathematics of . The moment you stop thinking about a single quantity and start thinking about lists of quantities — the pixels of an image, the features of a customer, the weights of a neural netwo
阅读文章 →Why this phase matters
Math Tooling FoundationsLinear algebra, calculus, probability, statistics, and the scientific Python stack3–5 weeksBuild the mathematical intuition that makes every later algorithm instead of feeling like magic. By the e
阅读文章 →Orientation
Core Machine LearningClassical models, evaluation, feature engineering, and tuning — implemented, not just imported6–8 weeksUnderstand classical ML deeply enough to implement the key algorithms from scratch and to build
阅读文章 →From linear models to neural networks
Deep Learning FoundationsNeurons, backpropagation, optimization, regularization, and PyTorch — from first principles6–8 weeksUnderstand neural networks from the ground up — forward pass, backpropagation, optimization — t
阅读文章 →Why images need special architectures
Computer VisionConvolutions, CNN architectures, transfer learning, detection, segmentation, and ViTs4–6 weeksUnderstand how neural networks see: the convolution operation, the architectural lineage from LeNet to ResNet t
阅读文章 →Why this is the highest-leverage phase
Sequence Models, NLP TransformersFrom RNNs to attention to LLMs, tokenization, fine-tuning, and RAG6–8 weeksMaster the architecture behind modern AI. Build a Transformer from first principles, understand tokenization (in
阅读文章 →Discriminative vs. generative
Generative ModelsAutoencoders, VAEs, GANs, and diffusion — how machines create4–5 weeksUnderstand how models learn to data: the latent-variable view (VAEs), the adversarial game (GANs), and the denoising process (diffusi
阅读文章 →A different learning paradigm
Reinforcement LearningMDPs, value functions, Q-learning, policy gradients, PPO, and RLHF3–4 weeks (optional)Understand learning by interaction and reward: Markov decision processes, the value/policy duality, deep Q-netwo
阅读文章 →Why MLOps is your edge
MLOps, Deployment Production SystemsExperiment tracking, serving, containers, monitoring, optimization, and CI/CD for ML4–6 weeksTurn models into reliable products. Track experiments, package and serve models, monitor fo
阅读文章 →The purpose of capstones
Capstone ProjectsCompounding value by building end-to-end systems in your own domainsOngoingConvert knowledge into demonstrable capability. Ship 2–3 end-to-end projects that intersect your existing domains (logistics, bi
阅读文章 →Preface: how to use this book
If linear algebra is the language of machine learning and calculus is its engine, then probability and statistics are its . Machine learning is, at its core, the discipline of drawing reliable conclusions from noisy, inc
阅读文章 →Distributions and Identities Reference
A compact reference for the notation, distributions, and identities used throughout the book.
阅读文章 →What Is Probability?
Probability is the mathematics of uncertainty — a precise language for reasoning about things we cannot predict with certainty. A coin flip, tomorrow's weather, whether an email is spam, what word comes next in a sentenc
阅读文章 →Conditional Probability and Bayes' Theorem
Almost all useful probability is : we want to know the chance of something what we already know. How likely is disease given a positive test? Spam given the word ``free''? The next word given the sentence so far? Conditi
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