Linear Algebra
Learn the linear algebra with applications 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 with applications in all fields, including vectors, matrices, linear transformations, eigenvalues, orthogonality, least squares, and SVD. Students will use Python and NumPy to connect mathematical theory with practical applications.
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 in different real life 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
Linear Systems and Mathematical Modelling
Lecture 02 — Matrices
Determinants, and Inverses.
Lecture 03 — Vector Spaces
Vectors, Linear Combinations, Span, and Subspaces.
Lecture 04 — Linear Independence
Basis, Dimension, and Rank
Lecture 05 — Transformations
Linear Transformations and Matrix Representations.
Lecture 06 — Orthogonality
Inner Products, Orthogonality, and Projections
Lecture 07 — Least Squares and Linear Regression
Inconsistent systems, normal equations, energy-demand prediction using Python
Lecture 08 — Eigenvalues, Eigenvectors, and Diagonalization
Matrix powers, Dynamic systems, Population-transition models and long-term behaviour.
Lecture 09 — Singular Value Decomposition, PCA, and Data Compression
Image compression, Dimensionality reduction and recommendation systems
Lecture 10 — Integrated Applications
Smart-city environmental monitoring, sensor-data analysis, integrated regression and PCA, smart-agriculture capstone.
Assignments
Quizzes
Case Study
Additional Resources
Reference Material
Supplementary mathematical learning material.
Useful Links
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