Linear Algebra For ML
Learn the linear algebra behind machine learning through practical concepts and applications. Use Python and NumPy to explore vectors, transformations, SVD, and data representation.
Course Description
This course introduces the essential linear algebra concepts used in machine learning, including vectors, matrices, linear transformations, eigenvalues, orthogonality, least squares, and SVD. Students will use Python and NumPy to connect mathematical theory with practical applications such as data representation, dimensionality reduction, and neural networks.
Topics include: Vectors and Vector Spaces, Matrix Operations and Linear Systems, Eigenvalues and Eigenvectors, Orthogonality and Least-Squares Methods, Singular Value Decomposition and Dimensionality Reduction
Course Learning Outcomes
Apply vectors, matrices, and linear transformations to represent machine-learning problems.
Solve systems of linear equations using analytical methods and Python.
Analyze data using eigenvalues, eigenvectors, orthogonality, and least-squares methods.
Implement SVD and dimensionality-reduction techniques for machine-learning applications.
Faculty
Dr Hira Benish
Associate Professor, Head of Mathematics Department
Riphah International University SahiwalCourse Outline
Course Outline
Official course outline and syllabus.
Lecture Notes
Lecture 01 — Introduction
Introduction and Linear Systems for Machine Learning
Lecture 02 — Vector Spaces
Vectors, Linear Combinations, Span, and Feature Spaces.
Lecture 03 — Linear Independence
Vector Spaces, Subspaces, Linear Independence, Basis, and Dimension.
Lecture 04 — Linear Transformations
Matrices as Linear Transformations, Composition, Inverses, and Geometric Effects.
Lecture 05 — Orthogonality
Inner Products, Orthogonality, Orthonormal Bases, and Vector Projections.
Lecture 06 — Least-Squares Problems
Least-Squares Problems, Normal Equations, Linear Regression, and Model Fitting
Lecture 07 — Eigenvalues, Eigenvectors
Eigenvalues, Eigenvectors, Diagonalization, and Stable Transformation Directions.
Lecture 08 — Singular Value Decomposition
Singular Value Decomposition, PCA, Low-Rank Approximation, and Data Compression.
Lecture 09 — Neural Networks
Neural Networks, Embeddings, Attention, and Gradient-Based Learning
Lecture 10 — Continuity
Integrated Machine-Learning Case Studies, Numerical Reliability, and Course Review.
Assignments
Quizzes
Case Study
Additional Resources
Reference Material
Supplementary mathematical learning material.
Useful Links
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