Linear Algebra for Machine Learning Workbook: Matrix Operations, Eigenvalues, SVD, Gradients, and Optimization

Linear Algebra for Machine Learning Workbook is a structured, problem-based workbook for students, practitioners, and researchers who want to build a strong mathematical foundation for machine learning. Instead of treating linear algebra as a series of abstract topics, this workbook connects every concept directly to the computations used in real machine learning systems.

Across 11 focused chapters, readers work through the core linear algebra and mathematical methods that appear throughout modern machine learning, from matrix multiplication and eigenvalues to singular value decomposition, gradients, probability, optimisation, and information theory. Every chapter is designed to develop genuine computational fluency through structured problems and worked solutions.

This workbook covers:

• Matrix multiplication, determinants, and inverses.
• Eigenvalues and eigenvectors.
• Singular value decomposition.
• Orthogonality and projections.
• Vector spaces, linear independence, and rank.
• Linear transformations.
• Matrix calculus and gradients.
• Probability and statistics for machine learning.
• Optimisation for machine learning.
• Information theory for machine learning.

This workbook is ideal for:

• Students preparing for machine learning courses or research.
• Practitioners who can implement models in code but want stronger mathematical understanding.
• Data scientists and engineers who want a clear, structured reference for the mathematics behind ML systems.
• Anyone working through deep learning or AI study paths who needs a solid linear algebra foundation.

If machine learning mathematics has ever felt unclear or hard to connect to real computations, this workbook gives you a direct, structured path from the fundamentals to the methods used in modern AI systems.