Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

A 2020 Vision of Linear Algebra

ocw.mit.edu

Post reply on HN
Print view View original

61–70 of 205 posts

Re: A 2020 Vision of Linear Algebra

#61

Post by [deleted] »

tchaffee wrote: post #59
auggierose wrote: post #23

Have not watched the videos yet, but that seems to me more like an 1820 vision of linear algebra :-) If you look at the order of topics in his book "An Introduction to Linear Algebra", you will find the topic "Linear Transformation" way back in chapter 8! Even after the chapters eigenvalue decomposition and singular value decomposition. But understanding that a matrix is just the representation of a linear transforma…

> Have not watched the videos yet, Then please do. I took several online linear algebra courses from sources I trust and they were pretty bad. Or let's put it another way: I'm a pretty clever guy and I was still left confused. Strang is excellent in the classroom, and I almost even like videos for learning now thanks to him (x1.5 speed is your friend). His videos should not be your only learning source, but judging h…

[deleted]

Re: A 2020 Vision of Linear Algebra

#62

Post by scared2 »

knzhou wrote: post #2

Gilbert Strang's linear algebra course blew my mind back in high school, and I still use insights from it every day. Strang has a particular lecturing style where he approaches every topic several times, often beginning many lectures before the main treatment. At first I thought it was a bit confusing, but later I realized it helped build fluency, just like a language class. I'm really thankful to MIT OCW for putting…

In High school?

Re: A 2020 Vision of Linear Algebra

#64

Post by michaelcampbell »

bluquark wrote: post #31
CameronNemo wrote: post #12

Earlier quoted context omitted.

Is there a better way to incentivize educational institutions to offer free content?

A modest proposal: ban donating to them so they need to radically increase their student body (online or offline) to earn their keep with tuition, instead of relying on the donations of the extremely rich parents of legacy admissions students.

I'm in an online Master's program now. With way more students than I feel they can handle. I'm sure they're milking the tuition just fine, but when projects and papers aren't graded in time to determine if you should withdraw or soldier on, it's less awesome.

While your view makes sense in the theoretical, once again human failings cause it to not work well in reality.

Re: A 2020 Vision of Linear Algebra

#65

Post by threatofrain »

enitihas wrote: post #35

Another good Linear Algebra book is "Linear Algebra Done Right", which Springer is giving for free right now. Link: https://link.springer.com/book/10.1007/978-3-319-11080-6

IMO Axler's book should be read either during or after you take an introductory course on Linear Algebra.

> You are probably about to begin your second exposure to linear algebra. Unlike your first brush with the subject, which probably emphasized Euclidean spaces and matrices, this encounter will focus on abstract vector spaces and linear maps.

Re: A 2020 Vision of Linear Algebra

#66

Post by pengaru »

It's ridiculous how much random college-level linear algebra textbook material I stared at before things clicked in the course of just jumping in and exploring 3D graphics and writing my own 3D vector, matrix multiplication and 3D transform headers and using them in making some games in plain C.

At some point it's like "Wait, is linear algebra really just about heaps of multiplication and addition? Like every dimension gets multiplied by values for every dimension, and values 0 and 1 are way more interesting than I previously appreciated. That funny identity matrix with the diagonal 1s in a sea of 0s, that's just an orthonormal basis where each corresponding dimension's axis is getting 100% of the multiplication like a noop. This is ridiculously simple yet unlocks an entire new world of understanding, why the hell couldn't my textbooks explain it in these terms on page 1? FML"

I'm still a noob when it comes to linear algebra and 3D stuff, but it feels like all the textbooks in the world couldn't have taught me what some hands-on 3D graphics programming impressed upon me rather quickly. Maybe my understanding is all wrong, feel free to correct me, as my understanding on this subject is entirely self-taught.

Re: A 2020 Vision of Linear Algebra

#67

Post by T-zex »

srean wrote: post #60
T-zex wrote: post #58

Earlier quoted context omitted.

I'm still a beginner and I think Strang's Linear algebra books are more like a supplement material to his lectures. If you need to build a solid theoretical foundation of linear algebra you'd need to consider other resources too. Having said that, he is explaining many things really well and is helping a lot to build intuition. He is always cautious presenting things that are computationally inefficient and suggests…

So the focus is on different recipes to cook a matrix with ? Different operations one can do on a matrix ? I hope its not just that, that would be very limiting considering what linear algebra is about and capable of.

No, his books are not recipes. The thing I'm struggling to communicate here is that he's got a more pragmatic style compared to other text books. The material he presents is complete and and he is doing great job making it approachable for non mathematicians.

His books usually expand on the subjects he presents at his online lectures. I see them as advanced lecture notes.

Re: A 2020 Vision of Linear Algebra

#68

Post by threatofrain »

tadhgds wrote: post #40
brmgb wrote: post #36

After watching this and having read the comments, I am quite puzzled by the approach American seem to take to linear algebra. Are matrices viewed as the core of the subject in the USA ? My country curriculum introduces linear algebra through group theory and vector spaces. Matrices come later.

I can't say whether or not it is the standard approach but I do know that it is very common in many countries to teach a linear algebra course that is heavy on matrix operations, that you can come away believing that linear algebra is somehow _about_ matrices and their operations. I know many in my university class seemed to believe that. A book I enjoyed is Axler's Linear Algebra Done Right[0], in which, if I rememb…

IMO Axler's book should be read either during or after you take an introductory course on Linear Algebra.

> You are probably about to begin your second exposure to linear algebra. Unlike your first brush with the subject, which probably emphasized Euclidean spaces and matrices, this encounter will focus on abstract vector spaces and linear maps.

Re: A 2020 Vision of Linear Algebra

#69

Post by Phlogistique »

pengaru wrote: post #66

It's ridiculous how much random college-level linear algebra textbook material I stared at before things clicked in the course of just jumping in and exploring 3D graphics and writing my own 3D vector, matrix multiplication and 3D transform headers and using them in making some games in plain C. At some point it's like "Wait, is linear algebra really just about heaps of multiplication and addition? Like every dimensi…

Is it the same issue as the infamous "monads tutorials" problem, where the understanding takes a lot of time to infuse but looks obvious in retrospect when it finally clicks?

Re: A 2020 Vision of Linear Algebra

#70

Post by vertak »

Can anyone grow why in the first 5 minutes of part 1 he shows a 3 by 3 matrix multiples by a 1 by 3 vector yet verbally he pulls out of no where this idea that if you have _two_ 1 by 3 vectors that pass through the origin then their linear combinations can be represented by a plane? The jump from the 3D to the 2D has me lost and I gave up
Post reply on HN