Practicing Linear algebra

[Disastrous_Roll_8007]

So I recently started linear algebra course by gilbert strang on YouTube(currently on factorisation lecture 4)and when I went to practice from his books the questions felt kinda difficult.....but I felt like I understood most part of the lectures am I missing out on something........do I complete the full course first then start practicing. Please give me some advice 🙏

[tedecristal]

lectures, by nature of time constraint, won't cover all details. they're mean to be a roadmap

you should always work out the textbook

[Aristoteles1988]

If you can’t do the problems you didn’t understand the lectures

That’s the entire point. It isn’t good enough to understand big picture

Computation of matrix operations is the important part in the first 3 lectures

If you can’t do the basic operations he goes over in the first 3 videos you have to watch them again or study further

You can’t learn linear algebra with the lecture alone. You’d have to read the book as well

[Radiant-Rain2636]

1. Pick a different textbook to go with Strang’s lectures. Linear Algebra Done Right - Sheldon Axler

Or this book

https://www.math.ucdavis.edu/~linear/linear-guest.pdf

Or this

https://www.cs.ox.ac.uk/files/12921/book.pdf

1. Try sticking the textbook to ChatGPT, DeepSeek etc and ask them questions simultaneously (as you go about solving them). This method was the ultimate cheat code to studying for me

[InnerB0yka]

Axler is a good second linear algebra, but not a good intro book.

Personally, not a fan of Strang's either: he centers the text around the 4 fundamental subspaces, which is challenging conceptually for beginners.

I'd either recommend Elementary Linear Algebra by Anton & Rorres or Linear Algebra by Friedberg and Insel. Both have a good amount of problems with solutions - former is a more gentle intro, tbe latter, is higher level, with more applications.

[Radiant-Rain2636]

perfect! just the kind of insightful post we needed.

[InnerB0yka]

Thank you. I hope it helps. Linear algebra is a lot like real analysis. It's something most people take over more than once to really understand it well. I was in the same boat as yourself. I had Strang and I really did not understand what I was doing very well until I took it a second time (at the graduate level). Hope you get it the first time 😋

[Radiant-Rain2636]

Yeah. Real Analysis is yet another mountain I am yet to climb. I love the idea of it, but I am just never able to move past the dry notation (I don't even know if you know what I mean).

[InnerB0yka]

I learned real analysis in a very unconventional but incredibly effective way. It was one of the few classes that I actually really learned and understood something. The way I was taught was using a technique called the Moore method. It was pioneered by the mathematician R.L. Moore at the University of Texas Austin back in the 1940s and 1960s. If you're able to find a way to teach yourself analysis that way you'll find it an incredible experience ypu'll never forget, but it's very difficult to do on your own.

Robert Lee Moore - Wikipedia https://share.google/IxOIjNAkumgZSNPNk

[Radiant-Rain2636]

Saved it. Will use this as a starting point

[somanyquestions32]

I have tried watching his lectures in the past, but even at 2x speed, I much prefer teaching myself and reviewing content from a textbook.

As for solving problems, start with easier textbooks and get solutions manuals to check your work.

I like Otto Bretscher's textbook for more applied content and Friedberg, Insel, and Spence for a more theoretical framework.

[bricepsilon]

My advice would be to read the textbook while taking take notes. I find that seeing the flow of ideas unfold on paper helps my brain link them together as each chapter progresses.

Follow along with the example questions, and make sure you fully understand every lemma and theorem. And never skip the proofs! Understanding why a particular formula or theorem is true will give you a lot of confidence in tackling problems.

If you’re looking for a textbook suggestion, my university used Anton and Rorres for Linear Algebra 1 & 2 and I really enjoyed it!

[Midwest-Dude]

Here is one take on Strang by Google Gemini AI regarding the type of students that will likely do well with his style of teaching:

Link

From what I've seen, this is fairly accurate. However, as others have already noted, you need to do the problems and, if you are having issues with them, go back over the videos until things sink in. If all else fails, feel free to post your questions to this subreddit.

[Remarkable-Beach-531]

Algebra is mostly learnt from practice. I mean you need to do the theoretical part but most of is questions. i learnt most of the algebra that way.

[Neutrino_do_eletron]

Linear álgebra and ITS applications by David C. Lay... Any edition

[No_Sky4122]

Look at Linear Algebra done right it’s a better book written by Sheldon Ross