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Chapters

This textbook is organized into 15 chapters covering 300 concepts across four major parts.

Part 1: Foundations of Linear Algebra

  1. Vectors and Vector Spaces - Introduces vectors as fundamental building blocks, covering operations, norms, and vector space theory.

  2. Matrices and Matrix Operations - Covers matrix notation, special types, and core operations including multiplication and inverse.

  3. Systems of Linear Equations - Methods for representing and solving linear systems using elimination and matrix techniques.

  4. Linear Transformations - How matrices represent geometric transformations including rotation, scaling, and projection.

Part 2: Advanced Matrix Theory

  1. Determinants and Matrix Properties - Determinant computation, properties, and geometric interpretation.

  2. Eigenvalues and Eigenvectors - Eigentheory fundamentals including characteristic polynomials and diagonalization.

  3. Matrix Decompositions - Matrix factorization methods including LU, QR, Cholesky, and SVD.

  4. Vector Spaces and Inner Products - Abstract inner product spaces, orthogonality, and least squares.

Part 3: Linear Algebra in Machine Learning

  1. Machine Learning Foundations - Data representation, PCA, linear regression, and gradient descent.

  2. Neural Networks and Deep Learning - Deep learning architecture, weight matrices, and backpropagation.

  3. Generative AI and Large Language Models - Embeddings, attention mechanisms, and transformer architecture.

  4. Optimization and Learning Algorithms - Optimization algorithms for training machine learning models.

Part 4: Computer Vision and Autonomous Systems

  1. Image Processing and Computer Vision - Image representation, convolution, filtering, and feature detection.

  2. 3D Geometry and Transformations - Three-dimensional geometry, quaternions, and camera models.

  3. Autonomous Systems and Sensor Fusion - Kalman filtering, SLAM, and autonomous navigation.

How to Use This Textbook

This textbook is designed for sequential learning - each chapter builds on concepts from previous chapters. The dependency structure ensures that prerequisite knowledge is always introduced before it's needed. While you can jump ahead to specific topics of interest, completing earlier chapters first will provide the strongest foundation.

Each chapter includes a list of concepts covered, allowing you to track your progress through the learning graph. Interactive microsimulations throughout the book help reinforce abstract mathematical concepts with visual, hands-on exploration.

Note: Each chapter includes a list of concepts covered. Make sure to complete prerequisites before moving to advanced chapters.