Linear Algebra is the mathematics of vector spaces and matrices. Apart from being used in all areas of theoretical mathematics, Linear Algebra has numerous other applications in various industries, ranging from data science, machine learning, computer graphics, economics to scientific computations.
Undoubtedly, Linear Algebra has become a prerequisite for advanced courses on various topics. Back in my college days, I remember Linear Algebra was one of the most popular mathematics courses at Columbia because students from various majors needed to take it.
If you did not have an opportunity to take it while in college or took it but struggled to understand the concepts, this will not be an issue anymore since you can now master Linear Algebra by taking high-quality online courses.
However, it may not be as simple as it seems. Some of those available are cash-grab courses that provide only basic training with few examples, which hardly help you grasp the essence of Linear Algebra.
I decided to do the heavy lifting for you. This article will only feature the best linear algebra courses that I found helpful in clarifying concepts and strengthening your problem-solving skills.
You can then select the right course based on your preferences and start learning right away.
Affiliate Disclosure: This article from Victory Tale contains affiliate links. We will receive a small commission if you purchase or enroll in Linear Algebra courses.
Nonetheless, we always value integrity and prioritize our audience’s interests. You can rest assured that we will present each course truthfully.
Things You Should Know
Prerequisites
Before taking Linear Algebra, you need to have solid background knowledge in basic math, particularly high-school-level algebra (equation solving, graphing, factoring, functions). Calculus may be helpful but not required.
However, some courses on the list will teach students how to apply Linear Algebra to real-life scenarios. There will be additional prerequisites for them which I will inform you specifically below.
Criteria
Below are the criteria for the best Linear Algebra courses
- Credible instructors
- User-friendly learning platform
- High-quality course materials
- Provide excellent value for money
- Mostly positive reviews from actual students
- My personal experience with the course, instructor, and learning platform (if any) must be positive.
1. Georgia Tech’s Linear Algebra Programs
Currently, Georgia Tech offers two Linear Algebra programs on edX. Both are essentially a college course separated into two parts. You will learn from Greg Mayer, a professor from the School of Economics.
With these high-quality lectures, course materials, and assessments, you will have a learning experience equivalent to enrolling on-site.
1.1) Introduction to Linear Algebra
This program comprises two minor courses as follows.
1. Linear Equations – The first course will drill deep into linear equations and systemic methods to help solve them. In the second part, you will learn about vectors and characterize them in terms of various aspects, including spans, linear combinations, relationships, etc.
Finally, you will explore linear independence and transformations, which are helpful in infinite real-world applications.
2. Matrix Algebra – The second course will be all about matrices. You will learn about the Inverse Matrix Theorem and explore other theorems and algorithms that allow you to apply Linear Algebra to more complicated issues involving multiple matrices.
Subsequently, you will learn how to apply matrix algebra to economics and computer graphics.
The program is 100% self-paced. Hence, you can freely set your learning schedule. However, Georgia Tech suggests spending 5-6 hours per week for two months on the program.
You can audit all the courses for free, but if you want your assignments to be graded and get a digital certificate upon program completion, you will need to pay $398 for a verified track.
1.2) Applications of Linear Algebra
The second program covers completely different content compared to the first. It focuses more on practical applications of Linear Algebra. You will learn how to use Linear Algebra to solve multiple real-world problems.
This program consists of two minor courses as follows:
Determinants and Eigenvalues – This course will first discuss determinants and their critical applications in computer graphics. You will use determinants to determine the amount of area changed by linear transformations.
In the second part, you will learn about eigenvalues and eigenvectors and understand their applications, including Markov chains.
Finally, you will work on a project that challenges you to create a transition matrix, a Markov chain, and a Google Matrix to calculate the page rank of the web.
Orthogonality & Symmetric Matrices and the SVD – The second course will focus on distance and orthogonality in the vector space.
After learning all the concepts, you will develop least-squares solutions for inconsistent systems and explore other least-squares problems that commonly arise in many practical applications.
Later, you will learn about matrix factorization and symmetric matrices and construct an orthogonal diagonalization and a spectral decomposition of a matrix.
The suggested pace is similar to that of the first course. You should spend 5-6 hours per week on the program, and you will complete it in two months.
Regarding pricing, you can also audit these two courses for free, while a verified track costs $398.
Pros & Cons
Pros
- Learn from a professor at a leading US university
- Well-structured curriculum
- Comprehensive: You will learn both the theorems and the applications in detail.
- Downloadable lecture slides + Easy-to-read transcripts
- Self-paced learning
- High-quality assignments and real-world projects
- Free auditing
Cons
- The verified track that provides a complete learning experience is costlier than all other alternatives.
2. UT Austin’s Linear Algebra Series
This series from the University of Texas-Austin offers another excellent training for Linear Algebra. Unlike other courses, you will learn Linear Algebra through UT Austin’s unique approach that utilizes visuals, illustrations, and computer programming.
The following courses constitute this series.
Note: You will be using MATLAB in this series. However, prior knowledge of MATLAB is not required for both courses.
2.1) Linear Algebra – Foundations to Frontiers
Below is what you will learn from the course.
- Vector and Matrix Operations
- Relationships between linear transformations, matrices, and linear equation systems
- Partitioned Matrices and Special Matrices
- Algorithms for Matrix computations to solve systems of equations
- Vector Spaces, Subspaces, and Linear Independence
- Orthogonality, Linear Least Squares, Eigenvalues, Eigenvectors
The suggested pace for this course is 6-10 hours weekly, and you will finish it in 15 weeks. If this pace requires too much weekly commitment, you can adjust it at will since the course is self-paced.
Auditing the course is free. However, an inexpensive verified track (costing only $49) may be a superior alternative.
2.2.) Advanced Linear Algebra: Foundations to Frontiers
The second course will drill deep into Linear Algebra for computing. You will grasp how data scientists use Linear Algebra to perform tasks in real life.
Below is a summary of what you will learn from the course.
- Orthogonalization + Use Singular Value Decomposition to decipher a matrix
- Solving Linear Systems and Least-Squares Problems
- Eigenvalues and Eigenvectors in computing
The suggested pace for this course even demands a higher weekly commitment than the first. To be specific, you should spend 8-12 hours per week for approximately 16 weeks. You can set your schedule if you cannot make it, though.
Auditing is again free of charge. However, the verified track, which offers graded assignments, costs only $49.
Pros and Cons
Pros
- One of the most comprehensive online Linear Algebra courses
- Learn from two leading professors of a renowned US university
- Unique approach that helps improve your understanding of Linear Algebra concepts and speeds up your computational ability
- Straightforward curriculum
- Informative but bite-sized video lessons
- Clear explanations
- High-quality course materials, containing downloadable notes, assignments, and exams
- Students will have an opportunity to solve Linear Algebra problems using coding.
- Affordable verified track for both courses + Free auditing
Cons
- Several sections can be extremely challenging for some students.
- This series may not be the best option for those unfamiliar with coding.
3. The Math of Data Science: Linear Algebra
If you are looking for a Linear Algebra course focusing on theories, this edX program from Rice University is probably your best bet.
Best of all, you will learn the logic behind all matrix and vector operations (such as matrix multiplication and inverses) so that you fully understand why they work in the way they do.
Course Content
The following is a summary of all course content.
- Linear Equations
- Vectors, Vector Space, Matrices, Linear Transformations
- Matrix, Vector Operations, and all the logic
- Basis and Dimensions
- Various real-world applications of Linear Algebra
- Inner Products and Orthogonality
The suggested pace is manageable. Rice recommends spending 6-8 per week for two months, perfect for students with full-time employment.
You can audit this course for free, while a verified track costs $159.
Coaching
If you live in the US and enroll in the verified track, you will access the coaching service for free.
Your coach will help you navigate the course, solve technical issues, keep you motivated, and explore career opportunities (if applicable).
Pros and Cons
Pros
- Learn from a professor at a leading US university
- Well-structured curriculum
- Clear explanations of all the logic behind Linear Algebra concepts
- Free auditing
- Coaching services are available for students who live in the US.
Cons
- The verified track is expensive compared to other alternatives.
- Currently unavailable (November 2021)
4. Become a Linear Algebra Master
If you are interested in learning Linear Algebra but want a more informal learning experience, I suggest picking up this Udemy course by Krista King.
Krista is an experienced math tutor and one of the most popular math instructors on Udemy. She has astounding teaching skills, which can make your math class more enjoyable.
Course Content
Below is a summary of what you will learn from this course.
- Operations on one and multiple matrices
- Matrices as vectors (Unit vectors, Linear combinations, Linear Independence in two and three dimensions, Linear Subspaces, Spans, Basis)
- Dot Products and Cross Products
- Matrix-Vector Products
- Deep dive into transformations
- Inverses, Determinants, and Transposes
- Orthogonality and Least-Squares Solutions
- Orthonormal bases and Gram-Schmidt Process
- Eigenvalues and Eigenvectors
The total length of all video lessons is 15 hours, which is more than sufficient to cover all the basic stuff in detail. However, the focus of this course is on solving problems. She will walk you through the most challenging problem in a step-by-step manner.
Besides the videos, Krista also provides summary notes for each lesson, a workbook, 400+ practice questions, and a final exam. These materials could be extremely helpful for college students who are preparing for an upcoming midterm or final exam.
Reviews: 4.8/5.0 from 20000+ students
Pros and Cons
Pros
- One of the most enjoyable Linear Algebra courses online
- Learn from a veteran math tutor with exceptional teaching skills
- Clear explanations of concepts and easy-to-follow walkthroughs for Linear Algebra problems
- Include detailed notes to help you understand Linear Algebra concepts
- Include 400+ practice questions and a final exam to test your knowledge
- Lifetime Access + 30-day money-back guarantee
- Inexpensive ($20 or even lower when on sale)
- In my opinion, the best course for students who struggle with Linear Algebra in college
Cons
- Krista does not utilize any professional graphics or animations that may be beneficial for some students to understand concepts more quickly. She will use hand-drawn graphics, which can be messy or confusing at times.
- Do not drill deep into advanced concepts or applications like other courses
5. Linear Algebra and Geometry 1/2
With more than 90 hours of video lessons, this series is probably the most informative Linear Algebra course available online. You will learn from Hania Uscka-Wehlou, who has experience teaching at several prestigious Swedish universities.
This series consists of two courses. You will need to purchase each separately.
5.1) Part 1
Below is a summary of what you will learn in the first course of the series.
- Vectors, Scalars, Linear Combinations, Matrices, Linear Transformations
- Systems of Linear Equations + How to Solve Them + Gaussian Equation
- Matrices and Matrix operations
- Deep dive into Inverses
- Linear Systems and Matrices
- All about Determinants
- Vectors (2-space, 3-space, n-space)
- Dot Product, Orthogonality, Orthogonal Projections
- Cross Products, Parallelograms, and Parallelepipeds
- Lines in R^2 and R^3
- Geometry of Linear Systems
- Distance between points, lines, and planes
- and many more
The first course alone is 46 hours long. Besides its high-quality video lessons, you will access 175 problems and detailed solutions (via video and text). Hence, you will have adequate resources to enhance your knowledge and skill.
Reviews: 4.9/5.0, Students: 950+
5.2) Part 2
The second course is slightly longer than the first (47 hours). It will explain in-depth the advanced concepts of matrices and vector spaces.
Below is a summary of the course content.
- Real Vector Spaces and Their Subspaces
- Linear Combinations and Linear Independence
- Coordinates, Basis, and Dimensions
- Row Space, Column Space, and Null Space
- Matrix Transformations from R^n to R^m
- Property of Matrix Transformations
- General Linear Transformations in different bases
- Gram-Schmidt Processes
- Orthogonal Matrices
- Eigenvalues and Eigenvectors
- Diagonalization
- and many more
Like the first course in the series, you will gain access to more than 150 problems and detailed solutions. Upon series completion, you will be ready for any Linear Algebra exam.
Reviews: 5.0/5.0, Students: 500+
Pros and Cons
Pros
- A strong candidate for the most informative and comprehensive Linear Algebra course online
- Learn from a highly knowledgeable instructor who taught at several leading European universities
- Well-structured curriculum
- Easy-to-follow explanations of fundamental concepts with tons of visualizations
- Fully packed with advanced examples and challenging exercises
- Lifetime Access + 30-day money-back guarantee
- Inexpensive ($20 or lower when on sale)
Cons
- Because of its immense content length, this course may not be optimal if you are looking for a crash course to review before the exam.
6. Complete Linear Algebra: Theory and Implementation in Code
This Udemy course by Mike X Cohen is excellent for those familiar with programming. Unlike most other courses, you will perceive how professionals implement real-world theories and concepts through MATLAB and Python.
Mike is a neuroscientist who owns a research lab funded by the US and European governments and is an associate professor at a Dutch university. With more than two decades of teaching experience, Mike can help you master Linear Algebra in no time.
Note: You should be familiar with MATLAB or Python before taking this course. Thus, absolute beginners might want to consider other alternatives instead.
Course Content
Below is a summary of what you will learn from the course
- Deep dive into vectors (Operations, Dot Product, Vector Length, Orthogonality, Subspace, Span, etc.)
- Introduction to Matrices (Operations, Matrix Rank, Spaces)
- Steps to solve Linear equations
- Determinant and Inverse
- Projections and Orthogonalization
- Least Squares for Model-fitting in statistics
- Eigendecomposition
- Singular Value Decomposition
- Quadratic form and definiteness
Within 34 hours of video lessons, you will mostly learn “applied” Linear Algebra in this course. Mike will use tons of visualizations that will help strengthen your geometric intuition of Linear Algebra.
In other words, you will “see” how Linear Algebra works and understand how professionals use software to solve real-world math problems. You will also have an opportunity to code independently and grasp how to utilize programming in scientific research.
Reviews: 4.8/5.0, Students: 22200+
Pros and Cons
Pros
- Excellent Linear Algebra course for those who want to get into data science and machine learning
- Learn from a veteran scientific researcher with more than two decades of teaching experience
- Strong focus on applied Linear Algebra
- Provide hands-on experience through coding and allow students to understand Linear Algebra intuitively
- Bite-sized lectures and sufficient assignments
- Clear explanations with excellent visualizations
- Lifetime Access + 30-day money-back guarantee
- Inexpensive ($20 or lower when on sale)
Cons
- The course does not focus on theories. In my opinion, learning Linear Algebra elsewhere may prove a better option.
- Some explanations can be too complicated for beginners since the instructor assumes that students already know MATLAB and Python programming.
Other Alternatives
Khan Academy – Khan Academy offers a free introductory course to help you learn essential concepts. However, this course will not be in-depth as paid ones.
Applications of Linear Algebra – This series from Davidson College offers thorough insights on Linear Algebra applications in computer graphics and data mining, which could be helpful for students who are into these two fields.
