Top books to learn linear algebra from beginner to advanced
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The primary question is: Why should I learn linear algebra if I aim to delve into Data Science? For aspiring citizen data scientists, linear algebra might not be the initial stepping stone. Nevertheless, for those looking to deeply grasp the mechanics “under the hood,” linear algebra is fundamental in data science. Much of the data in this field can be depicted as vectors (e.g., feature vectors) or matrices (e.g., data tables). Linear algebra offers the necessary tools to understand and manipulate these structures. It’s worth noting that one can build Machine Learning models or work on Data Science projects without an extensive understanding of linear algebra. However, a solid grounding in it can significantly enhance one’s intuition about the underlying processes. Show
“Linear Algebra: Step by Step” by Kuldeep Singh is a meticulously crafted guide to understanding the complexities of linear algebra. Singh’s approach is characterized by clarity and thoroughness, making the subject more approachable for both students and self-learners. The book aims to provide readers with a solid foundation, building up from basic concepts to more intricate topics in linear algebra. 2. Introduction to Linear Algebra “Introduction to Linear Algebra” by Gilbert Strang is a seminal work in the field, widely acclaimed for its intuitive approach and clarity of presentation. Strang, a celebrated professor and mathematician, brings his decades of teaching experience to the book, offering readers a deep yet accessible dive into the subject of linear algebra. 3. Linear Algebra Done Right “Linear Algebra Done Right” by Sheldon Axler is a refreshing take on the subject, sidestepping the traditional determinant-centric approach for a more intuitive understanding. Instead of beginning with matrices and determinants, Axler delves straight into vector spaces and linear maps. This approach lays a solid foundation, making more advanced topics like eigenvalues and eigenvectors seem like a natural progression rather than an abrupt introduction. The book covers a gamut of topics from inner product spaces, operators on these spaces, and the concept of determinants defined in an intuitive manner. Axler’s emphasis on proofs and theorems is balanced by his lucid explanations and illustrative examples. Bonus: No bullshit guide to linear algebra The “No bullshit guide to linear algebra” by Ivan Savov is a refreshingly straightforward introduction to linear algebra. As the title suggests, Savov’s approach is direct and unpretentious, aiming to make linear algebra accessible to readers without getting bogged down in unnecessary complexities. It’s an ideal read for beginners, self-learners, and anyone seeking a clear and concise overview of the subject. In summary, a good book for learning Linear Algebra by myself might be "Linear Algebra: A First Introduction" by Howard Anton or "Linear Algebra: A Second introduction" by Daniel Neuberger.
Summary: What would be a good book for learning Linear Algebra by myself in my situation (which is explained in my post below)? I did an undergraduate Linear Algebra course about 18 years ago. The textbook we used was Howard Anton’s “Elementary Linear Algebra”. The problem is that I never really got a real understanding of what I was doing even though I still managed to get an A. I could follow certain methods of computing things like eigenvectors and stuff. Still, as I said, I didn’t understand the concepts behind them or why I was computing what I was computing, or what was happening under the hood of those calculations. As an analogy, consider someone being able to follow certain procedures and compute integrals without really understanding that they are calculating the area under a curve or a volume. That’s what happened with my linear algebra course. The only thing I do remember understanding is how the Gaussian elimination method could solve a system of linear equations. Now I would like to really learn and understand the concepts behind the topics covered in a standard Linear Algebra course just for the sake of learning them. What would be a textbook or other resources like YouTube channels, etc. that would be appropriate for my needs?
I would approach in a three prong fashion:
You could use whatever book you're familiar with as either the primary or secondary as you work through the videos.
Another idea that usually gave me good results, is to search on Google with the key "Linear Algebra"+pdf, or "Linear Algebra"+lectures+pdf
I took a deep dive into learning the Linear Algebra that I didn't understand the first go-round in college (somehow it wasn't formally covered in my Mechanical Engineering curriculum, although obviously it was introduced ad hoc in some courses). It's been a wonderful experience working out the proofs of such magic as the determinant of a product is the product of the determinants, finally grokking what nullspace is, and learning why certain matrices have a full eigensolution - i.e., that they are normal matrices, and that Hermitian, skew-Hermitian & unitary matrices are always normal, and that the "2-sided" eigenproblem of [ K ] { x } = λ [ M ] { x } only works if the matrices are both Hermitian (which corresponds to its eigenvalues being real) and that [ M ] have all positive eigenvalues, with the reason being that to transform this eigenproblem into a "1-sided" one requires that [ M ]1/2 have real, non-zero eigenvalues (if an [ M ] eigenvalue is negative, that would introduce an imaginary component), and also only works because the product of Hermitian matrices is guaranteed to be Hermitian. (WHEW!) The responder has given some great sources.
Which book(s) did you use?
Depends on what your end goal is. That Anton book is one of the easiest introductions. I would work through it again, gaining familiarity with LA. Then use Lang: Linear Algebra with Berberian: Linear Algebra. Books complement each other. Berberian's LA text is written in the style of Axler's : Linear Algebra Done Right, before Linear Algebra Done Right was written. Lang goes through the determinant first approach, while Berberian goes through Linear Transforms first...
I can't remember off-hand. I have all my books on an external drive that I'll have to dig up.
I have written about 5 sets of linear algebra notes, 4 of which are on my webpage: https://www.math.uga.edu/directory/people/roy-smith Namely notes 1, 3,e,f, 6c, and 7, My latest, and perhaps most suitable, one is not there, but you can contact me via private message if you want to know more. It is an expansion of note 1 above from 15 pages to 127 pages. It seems my notes are somewhat eccentric, and few people have given me any feedback on them so that they may be unreadable.Thus perhaps a better option is the excellent notes of Sergei Treil at Brown: https://www.math.brown.edu/streil/papers/LADW/LADW-2014-09.pdf Last edited by a moderator: Oct 3, 2022
Of course, if you don't want a strictly bottom-up approach, you cam use the search function here and look up solved problems. If you have access to a college library, drop by and look up, browse through the books the Linear Algebra section, see which one feels right. A rule of thumb I think helps is that the author has a careful index of notation used. It likely reflects that the author made an effort to be clear. What is the best book on linear algebra?Linear. Before Machine Learning Volume 1 - Linear Algebra for A.I: The fundamental mathematics for Data Science and Artificial Inteligence. ... . Linear Algebra: Theory, Intuition, Code. ... . Essential Math for Data Science. ... . What Are Tensors Exactly? ... . Linear Algebra Done Right (Undergraduate Texts in Mathematics). What is the easiest way to learn linear algebra?An Intuitive Guide to Linear Algebra. Name the course Linear Algebra but focus on things called matrices and vectors.. Teach concepts like Row/Column order with mnemonics instead of explaining the reasoning.. Favor abstract examples (2d vectors! 3d vectors!) and avoid real-world topics until the final week.. Is linear algebra the hardest math class?When it comes to the different levels of mathematics, linear algebra ranks at the “intermediate level,” but is quite tough, similar to calculus II. That said, there are many other advanced courses like topology and abstract algebra. What is the best introductory linear algebra book reddit?For a first time introduction I highly suggest using Howard Anton's Elementary Linear Algebra. I would also accompany this text with Gilbert Strang's MIT open courseware. His videos focus more on the practical side of linear algebra and he is a fantastic teacher. |
