Linear Algebra Done Right
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- Type：Epub+TxT+PDF+Mobi
- Create Date：2021-04-10 14:53:38
- Update Date：2025-09-06
- Status：finish
- Author：Sheldon Axler
- ISBN：3319110799
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Summary
The long-awaited new novel from one of America’s most highly regarded contemporary writers， 'The Committed' follows the Sympathizer as he arrives in Paris as a refugee。 There he and his blood brother Bon try to escape their pasts and prepare for their futures by turning their hands to capitalism in one of its purest forms: drug dealing。
No longer in physical danger， but still inwardly tortured by his reeducation at the hands of his former best friend， and struggling to assimilate into a dominant culture， the Sympathizer is both charmed and disturbed by Paris。 As he falls in with a group of left-wing intellectuals and politicians who frequent dinner parties given by his French Vietnamese “aunt，” he finds not just stimulation for his mind but also customers for his merchandise ― but the new life he is making has dangers he has not foreseen， from the oppression of the state， to the self-torture of addiction， to the seemingly unresolvable paradox of how he can reunite his two closest friends， men whose worldviews put them in absolute opposition。
Both literary thriller and brilliant novel of ideas， 'The Committed' is a blistering portrayal of commitment and betrayal that will cement Viet Thanh Nguyen’s position in the firmament of American letters
No longer in physical danger， but still inwardly tortured by his reeducation at the hands of his former best friend， and struggling to assimilate into a dominant culture， the Sympathizer is both charmed and disturbed by Paris。 As he falls in with a group of left-wing intellectuals and politicians who frequent dinner parties given by his French Vietnamese “aunt，” he finds not just stimulation for his mind but also customers for his merchandise ― but the new life he is making has dangers he has not foreseen， from the oppression of the state， to the self-torture of addiction， to the seemingly unresolvable paradox of how he can reunite his two closest friends， men whose worldviews put them in absolute opposition。
Both literary thriller and brilliant novel of ideas， 'The Committed' is a blistering portrayal of commitment and betrayal that will cement Viet Thanh Nguyen’s position in the firmament of American letters
Reviews
Dorum
，
I really liked this book， but I think there is some room for improvement。 I will describe my reasoning below。 Nevertheless， among the arid and dry landscape of mathematics， this book is an oasis。The premise of the book is simple and outrageous at first sight。 Let us teach linear algebra without the use of determinants。 "Anathema！" I hear you all shout。 "It is impossible" （I heard myself think）。 However， Sheldon Axler proved me wrong。 And honestly， it makes things much more intuitive and easy。 Bu I really liked this book， but I think there is some room for improvement。 I will describe my reasoning below。 Nevertheless， among the arid and dry landscape of mathematics， this book is an oasis。The premise of the book is simple and outrageous at first sight。 Let us teach linear algebra without the use of determinants。 "Anathema！" I hear you all shout。 "It is impossible" （I heard myself think）。 However， Sheldon Axler proved me wrong。 And honestly， it makes things much more intuitive and easy。 But wait， isn't this like some sort of new math that would disable people to actually deal with determinants when encountering them elsewhere？ Not at all。 The very last chapter of the book is discussing determinants。 This goes all the way after discussing finite dimensional vector spaces， linear maps， kernels， images， inner product spaces， the spectral theorem， the Cayley Hamilton theorem， and everything else you would expect in a typical undergraduate level math course。Each chapter is having plenty of exercises to give the student a relatively good grasp on the concepts。 The book itself doesn't have the solutions， but they are available on a website。 All this make this book a favorite of mine in regards to this subject。 Nevertheless， it appears to me that there is some room for improvement。 I do understand the need for proof for every theorem。 The author has a point to make （i。e。 that linear algebra can be taught in a more efficient way by delaying the study of the determinants）。 What I would have improved though is the intuitive aspect of this branch of mathematics。I believe that the books is a step in the right direction， and of course， I know that exercises help。 However， I believe that due to the very abstract nature of this area of mathematics， some geometric approach of some kind， would have helped。 When I first learned linear algebra， a lot of the concepts seem simply introduced as definitions， without a reasoning behind the why and how。 As such， these courses were for me more of an exercise in memorization， and developed little practical understanding。 I was not able to understand why people were coming up with the concepts and names of linear algebra。Mathematics is notorious for its abstractness and that is the main reason behind it。 Consider the following （rather stupid） example that occurred to me when I first heard of the term "linear transforms" （linear mappings）: A linear mapping is a kind of function。 Of course， it has certain properties。 For example， if we have a linear mapping "f" on a vector space， then f（a）+f（b） = f（a+b）。 Also， m*f（a） = f（m*a） 。 The question that occurred to me， was this: "Why is a translation on a line not a linear transformation？"。 Of course， the simple answer is this: "It doesn't respect the properties above"。 （A translation is a function like this T（x） = x + c where c is a constant）But really， a translation is simply moving something in a straight line， from point A to point B。 It is the most obvious use of the word linear。 Of course， there are explanations and since then I came to know better。 Similar questions arise time and time again in the study of mathematics （why are eigenvalues so important？ What about the adjoint of an operator？ What is the idea behind them？ What is the intuition behind the dual spaces？ How come someone cared enough to name them？ etc。）To me it seems that a lot of these issues can and should be explained better。 I honestly don't believe these are stupid questions。 Of course， I don't believe that simply giving a simplistic reasoning would increase your capacity of problem solving。 However， this type of translation and understanding can certainly be done to great profit， and I believe it shortens the curve。 Also， I do know that many of the questions do not have a satisfying answer。 For example， I wasn't able to really understand why the mathematicians chose the term spectral for the spectral theorem。 I do know when it was used first， and who used it， but apparently there is no clear understanding as to why he used it or whether he saw any connections to physics。I believe that Sheldon Axler's book is a huge step in the right direction， but I feel that further strides can be easily done， and I believe that there is enough room for improvement。 At the moment at least， I think it is light years above my meager undergraduate course in explanatory power。 I believe he could have added more examples taken from geometry and physics。 。。。more
Mark Moon
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I enjoyed teaching out of this book this year， and expect to keep doing so for years to come。
Tara
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Excellent presentation of the material so far。 However， there is one glaring omission: no solutions to the exercises are provided。Fortunately， the bastards are available online here:https://linearalgebras。comQuite accurate thus far， though I’ve only checked through section 2B。 Excellent presentation of the material so far。 However， there is one glaring omission: no solutions to the exercises are provided。Fortunately， the bastards are available online here:https://linearalgebras。comQuite accurate thus far， though I’ve only checked through section 2B。 。。。more
Priya
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Hw can I read in tis app
Anlam Kuyusu
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This is the first math book I couldn't stop reading after the first few chapters。 I was hooked after the author's proof of the Rank-Nullity theorem - the elegance of the proof was superb。 The book also is the only book that gives a satisfactory theoretical explanation/justification of determinants。 （Hint: It's not pretty that's why it's eschewed。） This is the first math book I couldn't stop reading after the first few chapters。 I was hooked after the author's proof of the Rank-Nullity theorem - the elegance of the proof was superb。 The book also is the only book that gives a satisfactory theoretical explanation/justification of determinants。 （Hint: It's not pretty that's why it's eschewed。） 。。。more
Yash Patel
，
Oh man， this book is SO GOOD！ SO。 GOOD。 I learned linear algebra from https://www。goodreads。com/book/show/3。。。， but this book is SO MUCH better in terms of motivating any number of abstractions。 I'm not sure if it's because of my having becoming more familiar with abstraction since having read that book or if it's actually this book， but I thought this was far more approachable， without being any less rigorous。 It certainly went through all the same material， so all the material that I didn't un Oh man， this book is SO GOOD！ SO。 GOOD。 I learned linear algebra from https://www。goodreads。com/book/show/3。。。， but this book is SO MUCH better in terms of motivating any number of abstractions。 I'm not sure if it's because of my having becoming more familiar with abstraction since having read that book or if it's actually this book， but I thought this was far more approachable， without being any less rigorous。 It certainly went through all the same material， so all the material that I didn't understand the reasoning for （i。e。 considering the dual space and annihilators in that space or the permutation formulation of determinants or generalized eigenspaces） made so much more sense in reading this book。 There's also an ungodly number of exercises here， of which I probably did around 1/3。 They had a good range of difficulty， in the space of completely elementary if you understood the material to requiring a decent bit of thought to piece together some of the concepts。Anyway， that was a long enough rant。 But this book is GREAT 。。。more
Tianyao Chen
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Extremely lucid explanations for the abstract aspects of Linear Algebra including vector space， etc。 Read this for machine learning:D
Kent Sibilev
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A typical linear algebra textbook would start with the introduction of the matrixes and their various factorizations。 So you get a feeling that the whole purpose of the linear algebra is mostly in engineering and applied sciences。 This incredible book shows the 'algebra' part of the discipline。 I would definitely recommend it as a follow up to the standard approach to the subject。 A typical linear algebra textbook would start with the introduction of the matrixes and their various factorizations。 So you get a feeling that the whole purpose of the linear algebra is mostly in engineering and applied sciences。 This incredible book shows the 'algebra' part of the discipline。 I would definitely recommend it as a follow up to the standard approach to the subject。 。。。more
Guilherme Ari
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Decent Linear Algebra Book。
Jon
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There should be a subtitle "Thinking Like an Algebraist。" This is linear algebra from a mathematics perspective， not physics or engineering or anything else。 Even in math， it doesn't touch on analysis until the final chapter where he defines determinants。That said， the book is brilliant for its presentation。 The order of topics， examples and results makes so many things just "fall out。" For example， the proof Cauchy-Hamilton is pretty much "duh" and that of Jordan Canonical form is dead simple。I There should be a subtitle "Thinking Like an Algebraist。" This is linear algebra from a mathematics perspective， not physics or engineering or anything else。 Even in math， it doesn't touch on analysis until the final chapter where he defines determinants。That said， the book is brilliant for its presentation。 The order of topics， examples and results makes so many things just "fall out。" For example， the proof Cauchy-Hamilton is pretty much "duh" and that of Jordan Canonical form is dead simple。It's kinda like the first time you realize that trigonometry is really just the Pythagorean theorem， the unit circle， and some calculations。 。。。more
Coop Williams
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Get ready to write a lot of proofs。
John
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Good book。 UChicago should have required linear algebra for physics majors。
Chris
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lives up to its name。 And as the subhead says， this should not be your first introduction to linear algebra。All quants should read it eventually。 （I define a quant as anyone who uses matrices at work。）
Michael Yu
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This is a light and elegant overview of the subject ， good for those who want to get the concept quickly。
Diego Gomez
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Excellent introduction to linear algebra and abstract mathematics in general。
Bui
，
a great book for self-learning with reasonable and very beautiful proofs。 5 stars！
Xi Gong
，
A really great book！ It exposes me for the first time to the rigorous side of mathematics that I have long craved for。
Thanveer Ahamed
，
Excellent book！ Author's brilliance is reflected in this book。 An in-depth vision for mathematics for linear algebra made me fluent in it！ You may need 3 months to finish this book。 Since I'm a student at a college， it took me 1 year to finish but worth the time。 Must read！ Excellent book！ Author's brilliance is reflected in this book。 An in-depth vision for mathematics for linear algebra made me fluent in it！ You may need 3 months to finish this book。 Since I'm a student at a college， it took me 1 year to finish but worth the time。 Must read！ 。。。more
Reza
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one thing: u can trust other readers openion about this book。
Jared Tobin
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A solid reference for the core topics of linear algebra， and possibly the best option for those new to the subject。
Felix
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It's a nice book but I really don't understand why it goes to so much trouble to avoid determinants。From a purely aesthetic viewpoint there is something to be said for the approach， but in my experience teaching linear algebra 101 students don't have misgivings about using determinants。 They just don't know enough yet to realized something might be amiss so why bother？ It's a nice book but I really don't understand why it goes to so much trouble to avoid determinants。From a purely aesthetic viewpoint there is something to be said for the approach， but in my experience teaching linear algebra 101 students don't have misgivings about using determinants。 They just don't know enough yet to realized something might be amiss so why bother？ 。。。more
Anakurama
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Awesome book
Apoorv Vikram Singh
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An exceptional book on Linear Algebra。 Preferably a good read after some basic linear algebra course， so that you can actually appreciate the linear algebra in the book， and also have a mindfuck moment， when you relate it to your existing knowledge of linear algebra。
Walter
，
Excellent textbook for a second look at linear algebra from a strictly theoretical standpoint。 It size is small enough so that one may comfortably carry it around and promptly， effortlessly smack around fools that utter: "linear algebra！ that's just y = mx + b！！！ LOLZ"。 Their education is the responsibility of us all， and how often we forget the old ways。。。The proofs are clear but do require the reader to fill in some gaps。 This is intended。 Open to any page and witness the clarity that so oft Excellent textbook for a second look at linear algebra from a strictly theoretical standpoint。 It size is small enough so that one may comfortably carry it around and promptly， effortlessly smack around fools that utter: "linear algebra！ that's just y = mx + b！！！ LOLZ"。 Their education is the responsibility of us all， and how often we forget the old ways。。。The proofs are clear but do require the reader to fill in some gaps。 This is intended。 Open to any page and witness the clarity that so often escape the best efforts of a certain class of instructor; Axler will not suffer any unmotivated concepts。 Everything builds from previous definitions until there's just enough structure to flesh out the chapter objectives， thus there's little fat distract the reader。 Moreover， Axler is so badass that he does away with determinants until the last chapter of the book， he's so pimp he just didn't need any stinking determinants in his proofs。 That's right， the last chapter introduces trace and determinants and proceeds to bring everything together into a magnificent mic drop:I now finally understand why determinants are inextricably tied to notions of volume， and why we must multiply by the Jacobian when performing change of variables in multi-variable integrals， and so on。A newcomer to linear algebra will get very little of use here， save for the clearest definitions I've ever seen regarding the structure of vector spaces， subspaces and linear operators。 For a more applied/introductory approach to linear algebra， one can do much worse than Strang。I now feel much more comfortable moving onto a graduate-level Linear algebra course after visiting Axler's book， as such， it will be an invaluable reference moving forward。 。。。more
Christian
，
The third edition is an excellent update。 Previously the book was good， but the formatting and figures were subpar。 The third edition rectifies this， and it makes it much more of a joy to read。
Dmitri
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This is a great second book on linear algebra - something you might want to read once you read a foundation text on linear algebra first。 It is a full color book which makes the book rather expensive。 It's not a large book， but it's packed with just the right explanations and amount of theory to get you to understand the more mathematical aspects of linear algebra - the topics of spaces， linear maps and related theorems and concepts。 The book is very accessible， has plenty of exercises （no solut This is a great second book on linear algebra - something you might want to read once you read a foundation text on linear algebra first。 It is a full color book which makes the book rather expensive。 It's not a large book， but it's packed with just the right explanations and amount of theory to get you to understand the more mathematical aspects of linear algebra - the topics of spaces， linear maps and related theorems and concepts。 The book is very accessible， has plenty of exercises （no solutions though！） and is quite well designed。 。。。more
Ernst
，
A refreshing abstract approach to the subject （banishing determinants to the final chapter）， yet throughly readable with very slick proofs。 I would recommend it as a second book on LA。
Bob
，
The material started with Vector Spaces， which makes the most sense to me for linear algebra。 The text focus was more on "what is going on" and less on rigorous mathematics， making it a good reference for use with books that are more proof-oriented。The problem with linear algebra is its inherit difficulty: It is a subject that is extremely hard to really understand。 Despite much study， and a grad class， it still has me well into the level of very limited abilities。 Best thing？ Press on， and keep The material started with Vector Spaces， which makes the most sense to me for linear algebra。 The text focus was more on "what is going on" and less on rigorous mathematics， making it a good reference for use with books that are more proof-oriented。The problem with linear algebra is its inherit difficulty: It is a subject that is extremely hard to really understand。 Despite much study， and a grad class， it still has me well into the level of very limited abilities。 Best thing？ Press on， and keep working LOTS of problems 。。。 。。。more
Qiluoao
，
confusing:（
Jamie
，