Linear Algebra - Foundations to Frontiers

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9/10 stars
based on  180 reviews
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edX online courses
Harvard University, the Massachusetts Institute of Technology, and the University of California, Berkeley, are just some of the schools that you have at your fingertips with edX. Through massive open online courses (MOOCs) from the world's best universities, you can develop your knowledge in literature, math, history, food and nutrition, and more. These online classes are taught by highly-regarded experts in the field. If you take a class on computer science through Harvard, you may be tau...
Harvard University, the Massachusetts Institute of Technology, and the University of California, Berkeley, are just some of the schools that you have at your fingertips with edX. Through massive open online courses (MOOCs) from the world's best universities, you can develop your knowledge in literature, math, history, food and nutrition, and more. These online classes are taught by highly-regarded experts in the field. If you take a class on computer science through Harvard, you may be taught by David J. Malan, a senior lecturer on computer science at Harvard University for the School of Engineering and Applied Sciences. But there's not just one professor - you have access to the entire teaching staff, allowing you to receive feedback on assignments straight from the experts. Pursue a Verified Certificate to document your achievements and use your coursework for job and school applications, promotions, and more. EdX also works with top universities to conduct research, allowing them to learn more about learning. Using their findings, edX is able to provide students with the best and most effective courses, constantly enhancing the student experience.

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Sciences & Technology
Business & Management
21445 reviews

Course Description

Linear Algebra: Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:

  • It’s visual.
  • It connects hand calculations, mathematical abstractions, and computer programming.
  • It illustrates the development of mathematical theory. 
  • It’s applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you'll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignme...

Linear Algebra: Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:

  • It’s visual.
  • It connects hand calculations, mathematical abstractions, and computer programming.
  • It illustrates the development of mathematical theory. 
  • It’s applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you'll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.

MATLAB licenses will be made available to the participants free of charge for the duration of the course.

We invite you to LAFF with us!

Reviews 9/10 stars
180 Reviews for Linear Algebra - Foundations to Frontiers

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Student

10/10 starsCompleted
1 year, 11 months ago
Great introductory course on linear algebra. Use of the "slide-and-dice" system, instead of loops and indices, made linear algebra infinitely more comprehensible! This system is used in advanced linear algebra, and so is not a toy system just for introductory linear algebra, and is well worth learning. The instructors provide links to many papers and books that use this system to reinforce this point. The homework and exams are designed for self-study rather than for assessment. Full course notes in PDF format with links to course videos on youtube is available from a website setup by the instructors! After this course there is still more linear algebra to be learned, to cover what a typical undergraduate student in science and engineering is expected to know. I plan to use Gilbert Strang's book and MIT OCW course, to learn the topics left out of this course. This course gives me a good foundation for this. I wholehe... Great introductory course on linear algebra. Use of the "slide-and-dice" system, instead of loops and indices, made linear algebra infinitely more comprehensible! This system is used in advanced linear algebra, and so is not a toy system just for introductory linear algebra, and is well worth learning. The instructors provide links to many papers and books that use this system to reinforce this point. The homework and exams are designed for self-study rather than for assessment. Full course notes in PDF format with links to course videos on youtube is available from a website setup by the instructors! After this course there is still more linear algebra to be learned, to cover what a typical undergraduate student in science and engineering is expected to know. I plan to use Gilbert Strang's book and MIT OCW course, to learn the topics left out of this course. This course gives me a good foundation for this. I wholeheartedly recommend this course to everyone: you will get to learn the "slice-and-dice" method even if you already know linear algebra. My heartfelt thanks to the instructors for putting in an unbelievable amount of work to deliver this course, and that for free too!
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10/10 starsCompleted
  • 26 reviews
  • 24 completed
2 years ago
Definitely a 5 star course if others are . I have taken this course without the software part , and was able to fully follow the course teachings . I gained some great understanding that i had been longing for , through the course's Timmy-tools . So do not despair if you cannot run Matlab . To also learn software (algorithms) to aid mathematics , is an additional bonus this course has to offer , but no requirement for this course . Great course !
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Student

10/10 starsCompleted
1 year, 10 months ago
LAFF rekindled my love for math and is truly a model for how math should be taught, the structure of the course enables deep understanding and recognition of core topics as well as creating understanding that can be applied further. Robert and Maggie, thanks so much!
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2/10 starsCompleted
1 year, 11 months ago
Too much logic and I had trouble downloading the coding packages for Python. The videos were slow and technical and made the page load slowly. The problems need more words and pictures rather than purely algebraic ways of phrasing questions. Youtube's 3Blue1Brown Linear Algebra videos were better for conceptual understanding.
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10/10 starsCompleted
1 year, 11 months ago
Every thing is perfect. The teaching method and notes are excellent. The method to check the answers at the spot improve the capability and understanding of the topic. Thanks Saeed
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10/10 starsCompleted
1 year, 11 months ago
Very interesting content, but requires a strong mathematical background, especially if you wish to delve into the more complex areas. Robert does an excellent job walking through the concepts from basic to deeper ones. The evaluation could be made more challenging.
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10/10 starsCompleted
  • 2 reviews
  • 2 completed
1 year, 11 months ago
The instructors are great, the material is enough to get you up to speed but not that much for me to start losing motivation. The instructors are great, the videos tend to be straight to the point, the homeworks build a lot of intuition so I'd recommend *always* doing them. It's a great course overall. I was so happy with it I decided to opt for a certificate. It's my first MOOC certificate, yay!
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10/10 starsCompleted
1 year, 11 months ago
Instructors are seriously fantastic. In addition to informative, helpful and easy to understand, they also have excellent personalities. I also enjoyed that the course dabbles in to programming. I would highly recommend this course for anyone looking to learn linear algebra.
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Henry Harya profile image
Henry Harya profile image
8/10 starsCompleted
  • 6 reviews
  • 5 completed
1 year, 11 months ago
The lectures and reference material were excellent! It took a few weeks before it was clear what the purpose of some exercises were, like the programming exercises. There were some errors in the videos that they acknowledged and I hope they correct in future runs. Also, I would have preferred doing the course work in Python and hopefully that will be supported in the future as well.
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Student

6/10 starsCompleted
1 year, 11 months ago
The course is excellent for anyone interested in engineering and/or applied maths, economics, numerical analysis, etc.... Its main focus is computation and porgramming. I also liked the way the professor always motivated the topics before discussing them. However, it is not very useful for someone interested in analytical linear algebra, pure math, and as like, which for a person like me, made a great part of the course very boring.
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8/10 starsCompleted
  • 1 review
  • 1 completed
1 year, 11 months ago
Great course ! I've enjoyed it much. I'll be looking for the next steps. I had some hard times with some of the enrichments but I think I took the most important Cheers
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8/10 starsCompleted
1 year, 11 months ago
Great course. My only complaint is I wish it had gone even further. I really wish we could have gone more into the applications of eigenvalues and eigenvectors and given SVD some more thorough study. Guess I'll still have to take a few more courses...
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10/10 starsCompleted
  • 1 review
  • 1 completed
1 year, 11 months ago
This course really does what it's supposed to do - it gave me really solid foundations for linear algebra. Most topics were covered in depth. All explanations were clear to me. I suggest watching videos at 1.5 rate since 1.0 was way to slow for me. I recommend this course to anyone that wants to learn linear algebra.
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10/10 starsCompleted
2 years ago
Great introductory course on linear algebra. Interesting lectures, insightful exercises. Programming exercises greatly help understanding linear algebra concepts and algorithms, but this is not a programming course.
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10/10 starsCompleted
2 years ago
Excellent introductory course on linear algebra. The course content explains the concepts very well, with exercises that are calibrated to develop mastery. The format allows a student to determine what level of mastery they would like to attain--for example specializing in computation, algorithms, proofs or all the above. There are both advanced exercises and basic ones to develop intuition. Very much appreciate that this course is available for free. The instructors give top-notch instruction. They put much effort into it, as well as expertise gained through years of research and teaching. Thank you!
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8/10 starsCompleted
2 years, 2 months ago
The LAFF course used an interesting approach to present linear/matrix algebra content to a wide audience. Having taken math up to multivariable calculus, I was able to complete all assignments of this course within 3 weeks and hope to gain exposure prior to take calculus-based linear algebra. I found this course did an overall OK job. However, I would like to critique the PROGRAMMING portion of this course -- the course is missing the opportunity of furthering the MATLAB (or IPython). A lot of exercises were very insightful, however, with poor directions. The lectures were also quite dry. In addition, I believe the instructors could make the course more challenging by revoking access to some of the homework answers, certainly for the 3 exams. The course can also be improved by better organization: the concepts covered don't seem to require a full 12-week.
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kevin zhang profile image
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kevin zhang

10/10 starsTaking Now
2 years, 3 months ago
This course is awesome and it's the best course for all levels of learners! I wanna send a big thank you to all the stuff who make this course real!
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Patricio Barletta profile image
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Patricio Barletta

6/10 starsCompleted
2 years, 6 months ago
I find no flaw in the instructor, nor the provider; my review is about the content. Now, if you are (wannabe) a CS student and/or have never been exposed to college-level linear algebra, then this course may prove useful. But, if you mainly care about learning linear algebra then this course does a poor job. In that case I highly recommend Gilbert Strang course @ MIT OCW. I think the Professor made a sincere, and big, effort to develop a new way to teach linalg but, sadly, it just didn't work. Gilbert Strang teaches this same subject in a much more old fashioned way (him and the blackboard) and, god, what a great set of lessons.
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Claudio Felicioli profile image
Claudio Felicioli profile image
6/10 starsCompleted
  • 58 reviews
  • 58 completed
3 years ago
Elemental algebraic structures and algorithms are presented with a very strong focus on computation and time/space optimization. The content is very solid and interesting per se but, sadly, the lecture style is boring, the chosen programming environment is cumbersome and the assignments are only a little more than grinding.
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Student

10/10 starsCompleted
3 years, 1 month ago
I studied Linear Algebra as part of a Maths-Physiscs course some time ago. As a result of the teaching format in LAFF, I have a better understanding of the concepts. Video snippets followed by examples and exercises was more conducive to learning that an hour of reams of alpha-numerics on a whiteboard. I enjoyed the way you partition matrices when implementing algorithms. I just completed the matlab version but I am interested in looking over the iPython notebooks. Robert's favourite saying: 'go do the homework and I'll see you in the next video'. Aon duine ata ag iarriadh a chuid eolas matamataice a feabhsú, beir bua. Seo é an chursa.. Le gach dea-ghuI Jim Coen
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Osama Adel profile image
Osama Adel profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
3 years, 1 month ago
I've studied Linear Algebra before in my first year in college. However, this course here is something else. It really made me understand what Linear Algebra is; what are the meaning of the things I've always used blindly just to solve problems without really understanding what is going on. The contents are smoothly put, the instructor is very good, he just takes you step by step to master the topic. Although the course I've attended hadn't a serious grading, the homework helped me a lot to understand the materials and to understand not memorize the properties of special matrices for example. I recommend this course for anyone who didn't like Linear Algebra but realized its importance and cannot find the right place to learn it; this is what you're looking for.
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Student

10/10 starsCompleted
3 years, 1 month ago
The content was excellent, particularly for anyone with a computer science tilt. I particularly enjoyed two aspects of the course. The first was the focus on core principles that I had failed to learn previously taking linear algebra- two examples being that matrix-vector multiplication is *defined* as to represent a linear function / transformation and that matrix-matrix multiplication is *defined* as to represent linear function composition. The second aspect was the focus on proof writing- specifically in proving the correctness of algorithms. This is really where the course stands out those with a focus on Comp Sci.
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Floris Erich profile image
Floris Erich profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
3 years, 1 month ago
This was a great course! It goes into many relevant aspects of Linear Algebra and explains all the concepts very well. I loved the focus on algorithms and the MathLab homework. Also, I really liked how we explored the frontiers of Linear Algebra, making it feel like an interesting course both for people who haven't learned Linear Algebra yet as well as people who already have some experience.
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Quan Lin profile image
Quan Lin profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
3 years, 2 months ago
好吧,我更想用中文写: 非常,非常感谢这门课程的提供者,如此无私地提供高质量的课程. 我的背景是生物,并且在我的本科中并没有学习线性代数. 现在研究生物信息,才发现统计中太经常使用线性代数,所以我需要从头学起. 而这门课程,提供了一个非常好的平台,和学习材料,让我有机会学会线性代数. 由于我的目的并不是矩阵编程,所以我跳过了很多编程作业,对不起. 课程中的enrichment部分,对于我来说,很多地方也很难,我觉得我还需要回头再去读. 我太喜欢这门课程了!所有的作业都让我觉得确实有必要,有的时候是课没有听懂,材料也没看懂,然后做了作业才突然明白的!而且老师很有心有用心地设置每一个题目,配有视频讲解.难以找到比这设计更合理的课程了. 也是通过这门课程,我发觉了edX平台的长处,及时的练习确实比看完所有的视频再去做作业要合理(coursera上是这样的模式). 非常,非常感谢老师们的无私奉献!
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JISHNU BHATTACHARYA profile image
JISHNU BHATTACHARYA profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
3 years, 1 month ago
I did linear algebra longtime back in the college and also got exposure of the subject in econometrics and statistics course. But always I felt some gaps - this course provides a good link between usual approach plus programming intuition and why ? Stuff like Matrix Vector Multiplication, LU Decomposition and QR Decomposition , orthogonal projection etc. The course has been developed with a lot effort and research, it starts with simple intuition and builds up the concept very well and every exercise has been chosen for a specific purpose - to introduce a concept in the latter stage. Another unique part of the concept mainly emphasized by Robert is "understanding" matrix and vector by slicing and dicing - which gives an extra edge in visualization, why is happening and why. I would say anybody want to pursue econometrics , statistics and machine learning should start with this. After this course you will be a good position to p... I did linear algebra longtime back in the college and also got exposure of the subject in econometrics and statistics course. But always I felt some gaps - this course provides a good link between usual approach plus programming intuition and why ? Stuff like Matrix Vector Multiplication, LU Decomposition and QR Decomposition , orthogonal projection etc. The course has been developed with a lot effort and research, it starts with simple intuition and builds up the concept very well and every exercise has been chosen for a specific purpose - to introduce a concept in the latter stage. Another unique part of the concept mainly emphasized by Robert is "understanding" matrix and vector by slicing and dicing - which gives an extra edge in visualization, why is happening and why. I would say anybody want to pursue econometrics , statistics and machine learning should start with this. After this course you will be a good position to pursue those subjects at ease.
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Student

10/10 starsCompleted
3 years, 1 month ago
This is a Linear Algebra course that takes you - as promised - from foundations to frontiers. What you get from the course depends on whether your initial knowledge is closer to foundations or frontiers. I can only speculate - as I'm no beginner - that the course is very useful to every beginner who is at least slightly ambitious and self-disciplined. There are a lot of lessons with good explanations and tons of exercices. Some of them require a rigorous, more or less difficult proof - or a reasonable guess, but most are fairly simple and provide ample opportunity for training. Often the questions are designed to make you look for a pattern or a way to reuse a previous result. If you're closer to the frontier, the course may look less interesting, as it is being approached very late and possibly never reached. (Well, that's by design!) At the beginning, depending on your country, you may feel that you know most from school, but ev... This is a Linear Algebra course that takes you - as promised - from foundations to frontiers. What you get from the course depends on whether your initial knowledge is closer to foundations or frontiers. I can only speculate - as I'm no beginner - that the course is very useful to every beginner who is at least slightly ambitious and self-disciplined. There are a lot of lessons with good explanations and tons of exercices. Some of them require a rigorous, more or less difficult proof - or a reasonable guess, but most are fairly simple and provide ample opportunity for training. Often the questions are designed to make you look for a pattern or a way to reuse a previous result. If you're closer to the frontier, the course may look less interesting, as it is being approached very late and possibly never reached. (Well, that's by design!) At the beginning, depending on your country, you may feel that you know most from school, but even during the earlier lectures a new teacher and perspective may give you exciting insights. During the last lectures I learnt some new stuff, which had not or only very superficially treated in my own numerical mathematics course (destined for physicists and engineers) at university (SVD, SVD & OLS estimators). Even if "foundations to frontiers" is slightly exagerated: it starts from zero and goes beyond the level of many university-level courses. Thanks to Maggie Myers and Robert van de Geijn for offering this course!
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Student

10/10 starsCompleted
3 years, 2 months ago
Really great introduction class to linear algebra. The time and effort that Robert and Maggie has placed in this course is first class. With their step by step approach folks without a strong math background can easily follow the material (which is not diluted by any means). Would wholeheartedly recommend this course (this is from a person who has taken quite a few MOOCs).
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Tim Gasser profile image
Tim Gasser profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
3 years, 2 months ago
Excellent course for anyone interested in Linear Algebra. Split into 12 weeks, the first 8 weeks introduce you gently, and the final 4 weeks pick the pace up with juicy topics such as basis transforms and eigenvectors. Each week has an enrichment section to put the new knowledge in context and offer some more advanced applications. The lectures are very well put together, they are usually short and interspersed with homework questions to check you understood the video. This instant correction is really valuable. The exams have a practice exam first with video proofs which really help fill in gaps in knowledge. Having taken about 10 MOOCs, I was really impressed with how much time Robert and Maggie spent answering questions and helping out on the forums.
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Student

10/10 starsCompleted
3 years, 2 months ago
I took this course in the summer 2015 offering and I am very glad that I did. Even though I found the material challenging as I am in the declining years of my life, it was still worth the effort and it was very pleasing to be able to complete it. The course is nicely structured and presented in a student friendly style with (short) videos and accompanying script. There is also a pdf of the material available as well which contains some material additional to the video material. It is advisable to watch/read both. The videos are short enough for the student to absorb without being overwhelmed with new information. The material is organised into 12 sections. The first eight of these involved getting used to the FLAME notation and routines developed at UT Austin and putting them into practice in doing vector-vector operations, matrix-vector operations and matrix-matrix operations using Matlab. I found that having to program the o... I took this course in the summer 2015 offering and I am very glad that I did. Even though I found the material challenging as I am in the declining years of my life, it was still worth the effort and it was very pleasing to be able to complete it. The course is nicely structured and presented in a student friendly style with (short) videos and accompanying script. There is also a pdf of the material available as well which contains some material additional to the video material. It is advisable to watch/read both. The videos are short enough for the student to absorb without being overwhelmed with new information. The material is organised into 12 sections. The first eight of these involved getting used to the FLAME notation and routines developed at UT Austin and putting them into practice in doing vector-vector operations, matrix-vector operations and matrix-matrix operations using Matlab. I found that having to program the operations deepened my understanding of them. The remaining four sections were a step up in complexity, covering vector spaces, linear independence, bases, orthogonality, orthonormal bases, orthogonal projection, eigenvalues, eigenvectors and diagonalisation. In each section there were online exercises to be done. Apart from programming exercises there were also calculation and multiple choice exercises. These latter were cleverly designed to elicit the properties of vectors, matrices and their operations. In addition there were two midterm and one final exam. Preparing for these helped to consolidate the material. I found that I had to ask myself such questions as: How do you go about LU factorisation? How do you find a basis for the column space of a matrix? row space? null space? How do you go about QR factorisation? How do you handle an underdetermined system? an overdetermined system? How do you project onto a column space? How do you find eigenvalues? eigenvectors? How do you diagonalise a matrix? There was also a discussion forum where one could ask questions, make comments etc. The presenters Robert and Maggie were very prompt in replying. Their open-minded approach enhanced the feel good factor one got from this course.
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Peter Schoofs

10/10 starsCompleted
3 years, 2 months ago
Great course! It starts very simple but step by step it develops to college level or under graduate math. By using Matlab (free time limited student license for use during the course) you get a good insight in computations with matrices. But…programming, even with an easy and intuitive programming language, can be time consuming. It's not necessary but I could not resist to do all the assignments. The 8 hours a week became about16 hours. Many extra material is offered for those who like practical applications and have an interest in math papers. For those with an interest in Quantum Physics: this course introduces matrix calculations, vector spaces, shifting to another orthogonal basis, and in the last week explores matrices with eigenvalues and eigenvectors. It's a nice course to start with linear algebra, or refresh your memory and extent your knowledge.
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