Linear-Algebra-for-Data-Science
This course bridges the gap between abstract math and practical implementation by mapping vectors, matrices, and SVD straight to data science frameworks. By coding these concepts with Python and NumPy, you will gain the concrete skills needed to structure and manipulate complex datasets for predictive modeling.
Course Description
This course covers the practical linear algebra behind modern data science and machine learning. Instead of just memorizing proofs, you will work directly with vectors, matrices, linear transformations and SVD to explore practical applications such as data representation, feature engineering, dimensionality reduction and neural networks. We bridge the gap between math and code by using Python and NumPy to implement these concepts, giving you the concrete foundational skills needed to build and scale machine learning models from scratch.
Topics include: vectors, vector spaces, linear independence, Rank, Systems of Linear Equations, least square method, linear transformation, eigenvalue and eigenvector, singular value decomposition
Course Learning Outcomes
Comprehend the properties of matrices, including their determinants and rank
Apply the concepts of vector spaces and linear transformations to problems related to Computing
Apply the concept of Eigenvalues and vectors to solve problems related to Computing fields
Faculty
Dr. Muhammad Asad Iqbal
PhD Mathematics | Assistant Professor
Riphah International University, Sahiwal CampusCourse Outline
Course Outline
Official course outline and syllabus.
Lecture Notes
Lecture 01 — Vectors and its applications in Machine learning and Deep learning
This module introduces vectors and their practical applications, demonstrating how they serve as the mathematical foundation for neural network architectures, data prediction, and automated decision-making.
Lecture 02 — Matrices & Ranks applications in Machine learning
This module introduces matrices and matrix rank, demonstrating their essential roles in high-dimensional data representation and for image compression.
Lecture 03 — System of linear equations and its types
Introduce the system of linear equations and briefly discuss its types with real life examples
Lecture 04 — Solutions of systems of linear equations
Briefly discuss the types of solutions, and also discuss their algorithms
Lecture 05 — Positive definite matrix
Discuss all properties of positive definite matrix
Lecture 06 — Linear transformation
Briefly discuss linear transformations and its types
Lecture 07 — Linear transformation
Discuss the linear transformation problems in 1D to 4D
Lecture 08 — Eigenvalue and eigenvectors
Briefly discuss the eigenvalues and eigenvectors with problems
Lecture 09 — Singular value decomposition
Briefly discuss the singular value decompositions
Lecture 10 — Applications of eigenvalues and SVD
Applications of eigenvalues and SVD in robotics
Assignments
Quizzes
Case Studies
Additional Resources
Reference Material
Supplementary mathematical learning material.
Useful Links
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