MATH5110

MATH 5110: Applied Linear Algebra and Matrix Analysis

Welcome to the course page for MATH 5110: Applied Linear Algebra and Matrix Analysis.

Lecture Notes as an ebook: MATH 5110 E-Book

Course Overview

Linear algebra is one of the central languages of modern applied mathematics, data science, machine learning, optimization, scientific computing, and engineering.

In this course, we study both the theoretical foundations and computational tools of linear algebra, with emphasis on applications and mathematical understanding.

Interactive HTML Pages

Topics include:

Vector spaces and subspaces
Linear transformations and matrices
Rank, nullity, and systems of linear equations
Orthogonality and projections
Least squares problems
Eigenvalues and eigenvectors
Diagonalization and matrix decompositions
Singular value decomposition
Principal component analysis
Matrix norms and numerical considerations
Applications to data science, machine learning, networks, and topology

Repository Structure

MATH5110/
│
├── notes/          # Lecture notes and reading materials
├── homework/       # Homework assignments
├── labs/           # Python or MATLAB computer labs
├── projects/       # Course projects and project instructions
├── examples/       # Worked examples and supplementary files
└── README.md       # Course front page

The structure may be updated as the course develops.

Lecture Notes

Lecture notes will be posted regularly. They are intended to support classroom discussion and should be read together with the lectures.

Students are encouraged to:

Review definitions carefully
Work through examples by hand
Reproduce key computations
Connect algebraic formulas with geometric meaning
Use computation to test and visualize ideas

Homework

Homework assignments are designed to strengthen both theory and computation.

A typical homework problem may ask students to:

Prove a mathematical statement
Compute a basis, rank, null space, or projection
Interpret a matrix or linear transformation geometrically
Apply linear algebra to data or models
Use Python, MATLAB, or another computational tool

Unless otherwise stated, students should show enough work to explain their reasoning clearly.

Computer Labs

Computer labs are used to explore linear algebra through computation.

Possible tools include:

Python
NumPy
Matplotlib
scikit-learn
NetworkX
MATLAB

Labs may include applications such as:

Least squares approximation
Image compression
Principal component analysis
Spectral methods
Graphs and networks
Simplicial complexes and basic topological data analysis

Projects

Course projects connect linear algebra with real-world or research-inspired applications.

Possible project areas include:

Data analysis
Machine learning
Optimization
Networks
Imaging
Dynamical systems
Topological data analysis
Scientific computing

Project instructions and expectations will be posted in the projects/ folder.

Suggested Background

Students should be comfortable with:

Multivariable calculus
Basic matrix operations
Systems of linear equations
Elementary proof-writing
Some programming experience is helpful but not required at the beginning

Students who are less familiar with programming are encouraged to start early and ask questions.

How to Use This Repository

Students should regularly check this repository for updates.

Recommended workflow:

Read the lecture notes before or after class.
Work through examples independently.
Complete homework problems carefully.
Use labs to test computational ideas.
Review feedback and revise your understanding.

Academic Integrity

Students are encouraged to discuss ideas and learn from one another.

However, submitted work should reflect each student’s own understanding. Any collaboration, code, external resource, or AI assistance should be acknowledged according to course and university policies.

Instructor

He Wang
Department of Mathematics
Northeastern University

Updates

Course materials will be updated throughout the semester.

Please check this page and the relevant folders regularly.