14 ms·

This is good as a second course on Linear Algebra.For a first course,use (I am not kidding) Linear Algebra Done Wrong by Sergei Treil https://www.math.brown.ed

by ekm2 3y ago

This is good as a second course on Linear Algebra.For a first course,use (I am not kidding) Linear Algebra Done Wrong by Sergei Treil https://www.math.brown.edu/streil/papers/LADW/LADW.html https://www.math.brown.edu/streil/papers/LADW/LADW.html

endymi0n 3y ago
omg just had a look and this one is just everything I hate about mathematics and academia. Starts with lots of random definitions, remarks, axioms and introducing new sign language while completely disregarding introducing what it‘s supposed to do, explain or help with. All self-aggrandization by creating complexity, zero intuition and simplification. Isn‘t there anybody close to the Feynman of Linear Algebra?
- ekm2 3y ago
  There is no royal road bro
  - 77pt77 3y ago
    In his mind his above royals, so a royal road would be demeaning to him.
- PartiallyTyped 3y ago
  What about Axler’s then?
- gadrev 3y ago
  Gilbert Strang's course on Linear Algebra. Playlist: https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D Not as big in scope, though, but great introduction.
- bscphil 3y ago
  Yeah, a good example is on the second page of the first chapter: > Remark. It is easy to prove that zero vector 0 is unique, and that given v ∈ V its additive inverse −v is also unique. The is the first time the word "unique" is used in the text. Students are going to have no idea whether this is meant in some technical sense or just conventional English. One can imagine various meanings, but that doesn't substitute for real understanding. This is actually why I feel that mathematical texts tend to be not rigorous enough, rather than too rigorous. On the surface the opposite is true - you complain, for instance, that the text jumps immediately into using technical language without any prior introduction or intuition building. My take is that intuition building doesn't need to replace or preface the use of formal precision, but that what is needed is to bridge concepts the student already understands and has intuition for to the new concept that the student is to learn. In terms of intuition building, I think it's probably best to introduce vectors via talking about Euclidean space - which gives the student the possibility of using their physical intuitions. The student should build intuition for how and why vector space "axioms" hold by learning that fundamental operations like addition (which they already grasp) are being extended to vectors in Euclidean space. They already instinctively understand the axiomatic properties being introduced, it's just that the raw technical language being thrown at them fails to connect to any concept they already possess.
  - newprint 3y ago
    > Remark. It is easy to prove that zero vector 0 is unique, and that given v ∈ V its additive inverse −v is also unique. I'm sorry, this book is meant for the audience who can read and write proofs. Uniqueness proofs are staple of mathematics. If word "unique" throws you off, then this book is not meant for you.
    - curiousgal 3y ago
      No offense to OP but you are right. I get the feeling that people keep looking for a math-free resource to learn math...
      - CalChris 3y ago
        Now that would be unique.
        chaboud 3y ago
        It'll be the publication of the uncompleteness theorem... representation of math with no math.
      - RoyalHenOil 3y ago
        I think a lot of people just need an opportunity to see math demonstrated in a more tangible way. For example, I learned trig, calculus, and statistics from my science classes, not from my math classes (and that's despite getting perfect A's in all of my math classes). In math class, I was just mindlessly going through the motions and hating every second of it, but science classes actually taught me why it worked and showed me the beauty and cleverness of it all. I just needed to see the math to grok it.
        chongli 3y ago
        If you study mathematics at a rigorous level then you learn by writing proofs. Then you will rack your brain for hours or even days trying to figure out how to prove some simple things. It is not at all “going through the motions” at that point!
- aidos 3y ago
  3Blue1Browns Essence of Linear Algebra is my go to https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...
  - Grimblewald 3y ago
    I think this followed or accompanied by axler is the way to go
  - isaacfung 3y ago
    This, betterexplained, ritvikmath, SeeingTheory will give you a very solid math background(I think they are better than 90% of the intro math classes in colleges).
- resource0x 3y ago
  > Isn‘t there anybody close to the Feynman of Linear Algebra? No. The subject is too young (the first book dedicated to Linear Algebra was written in 1942). Since then, there have been at least 3 generations of textbooks (the first one was all about matrices and determinants). That was boring. Each subsequent iteration is worse. What is dual space? What motivates the definition? How useful is the concept? After watching no less than 10 lectures on the subject on youtube, I'm more confused than ever. Why should I care about different forms of matrix decomposition? What do they buy me? (It turns out, some of them are useful in computer algebra, but the math textbook is mum about it) My overall impression is: the subject is not well understood. Give it another 100 years. :-)
  - rq1 3y ago
    Why should it buy you something is the real question. You don't need to understand it the way the "initial" author thought about it, should that person had given it more thoughts... History of maths is really interesting but it's not to be confused with math. Concepts are not useful as you think about them in economic opportunity case. Think about them as "did you notice that property" and then you start doing math, by playing with these concepts. Otherwise you'll be tied to someones way of thinking instead of hacking into it.
    - resource0x 3y ago
      Your post represents a common viewpoint, but I don't agree with it. I'm a retired programmer trying to learn algebra for the purposes of education only. I am not supposed to take an exam or use the material in any material way, so to speak. I'd like to understand. Without understanding motivations and (on the opposite end) applications I simply lose interest. I happen to have a degree in math, and I know for the fact that when you know (or can reconstruct) the untuition behind the theory - it makes a world of a difference. If this kind of understanding is not a goal, then what is? BTW, by "buying" I din't mean that it should buy me a dinner, but at least it's supposed to tell me something conceptually important within the theory itself. Example: in the LADR book, the chapter on dual spaces has no consequences, and the author even encourages the reader to skip it :).
    - 3y ago
- bumbledraven 3y ago
  I like the free course on linear algebra by Strang’s Ph.D student Pavel Grinfeld. It's a series of short videos with online graded exercises. Most concepts are introduced using geometric vectors, polynomials, and vectors in ℝⁿ as examples. https://www.lem.ma/books/AIApowDnjlDDQrp-uOZVow/landing https://www.lem.ma/books/AIApowDnjlDDQrp-uOZVow/landing
- sealeck 3y ago
  I actually found the book quite intuitive and helpful in understanding linear algebra. It does explain a lot of the intuition for many definitions, as well as mathematical techniques. It's easy when presented with new things that you don't understand to reflexively dismiss them, but the ideas here are quite solid. It's also a textbook which aims to introduce students to a slightly higher level of mathematical thinking.
  - tnecniv 3y ago
    I self studied from this book as an undergrad. I was an EE major and took linear algebra as part of the mandatory ODEs class but didn’t “get it.” At a certain point, it became clear that if I wanted to learn the more advanced applied math I was interested in studying, I needed to really understand linear algebra. I thought Axler was great at introducing both the material and teaching me how to prove things rigorously. The month or so I spent that summer reading that book made the rest of the math I took in undergrad trivial.
- nabla9 3y ago
  Just because it's not for you does not mean it's not good. Some people have the intuition grasp mathematical concepts more easily than others. Some people don't see it and need to be motivated.
- mananaysiempre 3y ago
  The thing is, you can teach linear algebra as a gateway to engineering applications or as a gateway to abstract algebra. The second one will require a hell of a lot more conceptual baggage than the first one. It’s also what the book is geared towards. It is also intended for people who know something about the trade; it isn’t “baby’s first book on maths”. (Why can you graduate high school, do something labelled “maths” for a decade, and still be below the “baby’s first” level, incapable of reading basically any professional text on the subject from the last century? I don’t know. It’s a failure of our society. And I don’t even insist on maths being taught—but if they don’t teach maths, at least they could have the decency to call their stupid two-hundred-year-old zombie something else.) That conceptual baggage is not useless even in the applied context. For example, I know of no way to explain the Jordan normal form in 19th-century “columns or numbers” style preferred by texts targeted at programmers. (Not point at, not demonstrate, not handwave, explain—make it obvious and inevitable why such a thing must exist.) Or the singular value decomposition, to take a slightly simpler example. (Again, explain. You task, should you choose to accept it, is to see a pretty picture behind it.) And so on. Again, you can certainly live without understanding any of that. (To some extent. You’ll have a much harder time understanding the motivation behind PageRank then, say. And ordinary differential equations, classical mechanics, or even just multivariable calculus will look much more mysterious than they actually are.) But in that case you need a different book and a different teacher.
- anon-3988 3y ago
  This is why you should read the Preface: > It supposed to be a first linear algebra course for mathematically advanced students.
- danielvaughn 3y ago
  The Feynman of Linear Algebra is precisely what I want.
- seanhunter 3y ago
  A lot of people think Gil Strang was that. Certainly his 18.06SC lecture series is fabulous.[1] I really like Sheldon Axler and he has made a series of short videos to accompany the book that I think are wonderful. Very clear and easy to understand, but with a little bit more of the intuition behind the proofs etc. [1] https://youtube.com/playlist?list=PL221E2BBF13BECF6C&si=G2XqE-itCFzQt7VE https://youtube.com/playlist?list=PL221E2BBF13BECF6C&si=G2Xq... and https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011/ https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011... [2] https://linear.axler.net https://linear.axler.net is his website for the book https://linear.axler.net/LADRvideos.html https://linear.axler.net/LADRvideos.html Is the videos directly although he says the update to the videos to correspond with edition 4 is going to happen 23 Dec.
- mayd 3y ago
  > Isn‘t there anybody close to the Feynman of Linear Algebra? That would probably be Gilbert Strang. While, as a maths person I would prefer a bit more rigour, his choice of topics and his teaching skill make his the most outstanding introductory course I have seen. I would run a mile from any course that disrespects determinants. And that includes Axler's! Also I wish more Linear Algebra courses would cover Generalized Inverses.
- penguin_booze 3y ago
  I strongly echo the sentiment. I had a look at the book earlier and thought 'this is not the way to do anything, let alone linear algebra'. He may not be Feynmann, but I'd recommend Pavel's Linear Algebra series: https://www.youtube.com/watch?v=Fnfh8jNqBlg&list=PLlXfTHzgMRUKXD88IdzS14F4NxAZudSmv https://www.youtube.com/watch?v=Fnfh8jNqBlg&list=PLlXfTHzgMR.... He does a lot of time developing intuition in the early hours.
- byli 3y ago
  As mentioned, the book was intended to be a "second course" in linear algebra. I personally self-studied out of the 3rd edition of Axler, and found it very helpful for understanding exactly what is going on with all the matrix computations we do. Plus, the same can be said about artists. After all, it's all self-aggrandization, and art is not made to be simple or intuitive.
anta40 3y ago
Amusing title. And by skimming at the table of contents, guess that's how I learnt linear algebra many years ago as an undergrad student. Guess I need to re-learn it again.

by ekm2 3y ago

endymi0n 3y ago

omg just had a look and this one is just everything I hate about mathematics and academia. Starts with lots of random definitions, remarks, axioms and introducing new sign language while completely disregarding introducing what it‘s supposed to do, explain or help with. All self-aggrandization by creating complexity, zero intuition and simplification. Isn‘t there anybody close to the Feynman of Linear Algebra?

ekm2 3y ago
There is no royal road bro
- 77pt77 3y ago
  In his mind his above royals, so a royal road would be demeaning to him.
PartiallyTyped 3y ago
What about Axler’s then?
gadrev 3y ago
Gilbert Strang's course on Linear Algebra. Playlist: https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D Not as big in scope, though, but great introduction.
bscphil 3y ago
Yeah, a good example is on the second page of the first chapter: > Remark. It is easy to prove that zero vector 0 is unique, and that given v ∈ V its additive inverse −v is also unique. The is the first time the word "unique" is used in the text. Students are going to have no idea whether this is meant in some technical sense or just conventional English. One can imagine various meanings, but that doesn't substitute for real understanding. This is actually why I feel that mathematical texts tend to be not rigorous enough, rather than too rigorous. On the surface the opposite is true - you complain, for instance, that the text jumps immediately into using technical language without any prior introduction or intuition building. My take is that intuition building doesn't need to replace or preface the use of formal precision, but that what is needed is to bridge concepts the student already understands and has intuition for to the new concept that the student is to learn. In terms of intuition building, I think it's probably best to introduce vectors via talking about Euclidean space - which gives the student the possibility of using their physical intuitions. The student should build intuition for how and why vector space "axioms" hold by learning that fundamental operations like addition (which they already grasp) are being extended to vectors in Euclidean space. They already instinctively understand the axiomatic properties being introduced, it's just that the raw technical language being thrown at them fails to connect to any concept they already possess.
- newprint 3y ago
  > Remark. It is easy to prove that zero vector 0 is unique, and that given v ∈ V its additive inverse −v is also unique. I'm sorry, this book is meant for the audience who can read and write proofs. Uniqueness proofs are staple of mathematics. If word "unique" throws you off, then this book is not meant for you.
  - curiousgal 3y ago
    No offense to OP but you are right. I get the feeling that people keep looking for a math-free resource to learn math...
    - CalChris 3y ago
      Now that would be unique.
      - chaboud 3y ago
        It'll be the publication of the uncompleteness theorem... representation of math with no math.
    - RoyalHenOil 3y ago
      I think a lot of people just need an opportunity to see math demonstrated in a more tangible way. For example, I learned trig, calculus, and statistics from my science classes, not from my math classes (and that's despite getting perfect A's in all of my math classes). In math class, I was just mindlessly going through the motions and hating every second of it, but science classes actually taught me why it worked and showed me the beauty and cleverness of it all. I just needed to see the math to grok it.
      - chongli 3y ago
        If you study mathematics at a rigorous level then you learn by writing proofs. Then you will rack your brain for hours or even days trying to figure out how to prove some simple things. It is not at all “going through the motions” at that point!
aidos 3y ago
3Blue1Browns Essence of Linear Algebra is my go to https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...
- Grimblewald 3y ago
  I think this followed or accompanied by axler is the way to go
- isaacfung 3y ago
  This, betterexplained, ritvikmath, SeeingTheory will give you a very solid math background(I think they are better than 90% of the intro math classes in colleges).
resource0x 3y ago
> Isn‘t there anybody close to the Feynman of Linear Algebra? No. The subject is too young (the first book dedicated to Linear Algebra was written in 1942). Since then, there have been at least 3 generations of textbooks (the first one was all about matrices and determinants). That was boring. Each subsequent iteration is worse. What is dual space? What motivates the definition? How useful is the concept? After watching no less than 10 lectures on the subject on youtube, I'm more confused than ever. Why should I care about different forms of matrix decomposition? What do they buy me? (It turns out, some of them are useful in computer algebra, but the math textbook is mum about it) My overall impression is: the subject is not well understood. Give it another 100 years. :-)
- rq1 3y ago
  Why should it buy you something is the real question. You don't need to understand it the way the "initial" author thought about it, should that person had given it more thoughts... History of maths is really interesting but it's not to be confused with math. Concepts are not useful as you think about them in economic opportunity case. Think about them as "did you notice that property" and then you start doing math, by playing with these concepts. Otherwise you'll be tied to someones way of thinking instead of hacking into it.
  - resource0x 3y ago
    Your post represents a common viewpoint, but I don't agree with it. I'm a retired programmer trying to learn algebra for the purposes of education only. I am not supposed to take an exam or use the material in any material way, so to speak. I'd like to understand. Without understanding motivations and (on the opposite end) applications I simply lose interest. I happen to have a degree in math, and I know for the fact that when you know (or can reconstruct) the untuition behind the theory - it makes a world of a difference. If this kind of understanding is not a goal, then what is? BTW, by "buying" I din't mean that it should buy me a dinner, but at least it's supposed to tell me something conceptually important within the theory itself. Example: in the LADR book, the chapter on dual spaces has no consequences, and the author even encourages the reader to skip it :).
  - 3y ago
bumbledraven 3y ago
I like the free course on linear algebra by Strang’s Ph.D student Pavel Grinfeld. It's a series of short videos with online graded exercises. Most concepts are introduced using geometric vectors, polynomials, and vectors in ℝⁿ as examples. https://www.lem.ma/books/AIApowDnjlDDQrp-uOZVow/landing https://www.lem.ma/books/AIApowDnjlDDQrp-uOZVow/landing
sealeck 3y ago
I actually found the book quite intuitive and helpful in understanding linear algebra. It does explain a lot of the intuition for many definitions, as well as mathematical techniques. It's easy when presented with new things that you don't understand to reflexively dismiss them, but the ideas here are quite solid. It's also a textbook which aims to introduce students to a slightly higher level of mathematical thinking.
- tnecniv 3y ago
  I self studied from this book as an undergrad. I was an EE major and took linear algebra as part of the mandatory ODEs class but didn’t “get it.” At a certain point, it became clear that if I wanted to learn the more advanced applied math I was interested in studying, I needed to really understand linear algebra. I thought Axler was great at introducing both the material and teaching me how to prove things rigorously. The month or so I spent that summer reading that book made the rest of the math I took in undergrad trivial.
nabla9 3y ago
Just because it's not for you does not mean it's not good. Some people have the intuition grasp mathematical concepts more easily than others. Some people don't see it and need to be motivated.
mananaysiempre 3y ago
The thing is, you can teach linear algebra as a gateway to engineering applications or as a gateway to abstract algebra. The second one will require a hell of a lot more conceptual baggage than the first one. It’s also what the book is geared towards. It is also intended for people who know something about the trade; it isn’t “baby’s first book on maths”. (Why can you graduate high school, do something labelled “maths” for a decade, and still be below the “baby’s first” level, incapable of reading basically any professional text on the subject from the last century? I don’t know. It’s a failure of our society. And I don’t even insist on maths being taught—but if they don’t teach maths, at least they could have the decency to call their stupid two-hundred-year-old zombie something else.) That conceptual baggage is not useless even in the applied context. For example, I know of no way to explain the Jordan normal form in 19th-century “columns or numbers” style preferred by texts targeted at programmers. (Not point at, not demonstrate, not handwave, explain—make it obvious and inevitable why such a thing must exist.) Or the singular value decomposition, to take a slightly simpler example. (Again, explain. You task, should you choose to accept it, is to see a pretty picture behind it.) And so on. Again, you can certainly live without understanding any of that. (To some extent. You’ll have a much harder time understanding the motivation behind PageRank then, say. And ordinary differential equations, classical mechanics, or even just multivariable calculus will look much more mysterious than they actually are.) But in that case you need a different book and a different teacher.
anon-3988 3y ago
This is why you should read the Preface: > It supposed to be a first linear algebra course for mathematically advanced students.
danielvaughn 3y ago
The Feynman of Linear Algebra is precisely what I want.
seanhunter 3y ago
A lot of people think Gil Strang was that. Certainly his 18.06SC lecture series is fabulous.[1] I really like Sheldon Axler and he has made a series of short videos to accompany the book that I think are wonderful. Very clear and easy to understand, but with a little bit more of the intuition behind the proofs etc. [1] https://youtube.com/playlist?list=PL221E2BBF13BECF6C&si=G2XqE-itCFzQt7VE https://youtube.com/playlist?list=PL221E2BBF13BECF6C&si=G2Xq... and https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011/ https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011... [2] https://linear.axler.net https://linear.axler.net is his website for the book https://linear.axler.net/LADRvideos.html https://linear.axler.net/LADRvideos.html Is the videos directly although he says the update to the videos to correspond with edition 4 is going to happen 23 Dec.
mayd 3y ago
> Isn‘t there anybody close to the Feynman of Linear Algebra? That would probably be Gilbert Strang. While, as a maths person I would prefer a bit more rigour, his choice of topics and his teaching skill make his the most outstanding introductory course I have seen. I would run a mile from any course that disrespects determinants. And that includes Axler's! Also I wish more Linear Algebra courses would cover Generalized Inverses.
penguin_booze 3y ago
I strongly echo the sentiment. I had a look at the book earlier and thought 'this is not the way to do anything, let alone linear algebra'. He may not be Feynmann, but I'd recommend Pavel's Linear Algebra series: https://www.youtube.com/watch?v=Fnfh8jNqBlg&list=PLlXfTHzgMRUKXD88IdzS14F4NxAZudSmv https://www.youtube.com/watch?v=Fnfh8jNqBlg&list=PLlXfTHzgMR.... He does a lot of time developing intuition in the early hours.
byli 3y ago
As mentioned, the book was intended to be a "second course" in linear algebra. I personally self-studied out of the 3rd edition of Axler, and found it very helpful for understanding exactly what is going on with all the matrix computations we do. Plus, the same can be said about artists. After all, it's all self-aggrandization, and art is not made to be simple or intuitive.

anta40 3y ago

Amusing title. And by skimming at the table of contents, guess that's how I learnt linear algebra many years ago as an undergrad student. Guess I need to re-learn it again.