Hi : what are the best book(s) to learn Linear Algebra from that is friendly and intuitive for ML?
I’ve gone through several and none I’ve found really great for modern applications. The Strang book is a classic – really great for beginners, but more “traditional” and focused on theory.
In fact, the absence of a great book is what motivated me to make my linear algebra course.
Of course, there might be a great linear algebra book in the near future…
not a book but do you know 3blue1brown on youtube? His animations are amazing and really gives you an insight. Or have you heard of MikeXCohen? He has some great courses on Udemy and on his website.
3blue1brown is indeed great. Not sure about this MikeXCohen guy, though. I heard he has a really bizarre sense of humor.
Seriously, though, learning from an actual physical textbook is quite different from learning online. Both have advantages, and I think a great book is a unique learning experience beyond a great online course.
There is a course by Gilbert Strang Matrix Methods in Data Analysis, Signal Processing, and Machine Learning
The Course is accompanied by his book Linear Algebra and Learning from Data
He’s also the author of a more general book “Linear Algebra and Its Applications” which is quite popular
The classic Strang book is great and I recommend it – that’s what I was referring to in my comment above.
I haven’t watched the lectures for the new course, but I did buy the book. Not worth it, unfortunately. It reads like his lecture notes, and I think would be really difficult for someone to understand if they didn’t already know the material.
My recommendation is “Linear Algebra for Calculus” by K.Heuvers, et al.
I have gone through this complete series ( I may be Biased since I’m studying in IISc-Bengaluru) and hence can vouch for it. It’s slightly advance, and more geared towards the theoretical side. And these lectures are meant for graduate-level studies. They have especially covered SVD in great depth, and once you understand that, you can develop your code for handling/solving any general m*n matrix.
You can supplement your studies further by reading the text, “Linear Algebra Done Right” by Sheldon Axler. I would not call this call to be exactly, “friendly”, but if you want to understand the various ML algorithms, at the fundamental level, then you should go through it. Let me warn you, This text is, mathematically quite intense. You’ll have to sit down with a pen and paper and workout out the missing steps in the derivations. The text and it’s solution manual are both available on ’ libgen ', and ’ z - library ', for free.
If this is the first time you are studying Linear algebra, then I suggest you first go through Dr. Cohen’s course on Linear algebra, then MIT’s 18.06, then MIT’s 18.065, and then if you still motivated to learn more, then you go through the series and text which I have mentioned. If you already have some exposure, then go for it directly.
I know it’s a lot of work, but trust me Linear algebra is worth it. Once you go through it you’ll realize how seemingly different fields of fluid mechanics ( specifically direct numerical simulations (DNS) of Navier-stokes equations, ) stability analysis of any general system, electrodynamics( classical and quantum both), quantum mechanics, control theory, statistical thermodynamics, signal processing, numerical analysis/solution of ODEs-PDEs etc, are beautifully and elegantly connected at such a fundamental level. ( assuming you are exposed to relevant ideas )
You’ll be amazed to see that the techniques which allow us to model the electrical signals of the brain ( Fourier series or Fourier transform whatever’s appropriate for the given situation) are quite similar, to those, which allows to directly solve ( numerically, in frequency domain ) the formidable Navier-Stokes equation, from which you could calculate the stresses and hence the forces which blood exerts while flowing in a blood vessel. Even, when there’s some blockage in the artery ( as happens when fats get deposited in the artery or in the case of Atherosclerosis etc ) and flow inside of it is turbulent( A very formidable problem!! You’ll have to study soft wall turbulence if you want to know-how ). Now I don’t know about you, but this seems pretty fascinating to me. This is just an example. I could go on and on endlessly, but you get the point.
So if you are interested to enter the beautiful and absolutely gorgeous world of Linear Algebra, then Welcome abroad.
Good luck with your future endeavors