[rahimnathwani]

I don't know whether LADR is good for someone who is new to linear algebra. I've seen it recommended so many times, so ~12 years ago when I was living in Beijing I bought two copies (one in English for me, and one in Chinese in case I needed to ask a colleague for help).

It took me time to study each page, to understand the examples, and then to attempt the exercises. It seemed very beautiful.

Then one day I came to a part I couldn't understand: I didn't see how something Axler said followed from the earlier stuff on the page actually followed. I scratched my head for a couple of hours, which is much longer than I'd spent on any previous page.

Eventually I asked a colleague for help. I showed him the page. He asked me to explain what I didn't understand. I started to explain what I knew, and how I didn't understand how this thing followed. As I was explaining it, that part suddenly clicked.

But I got stuck a few more times and didn't persevere.

I wonder whether it would have been better for me to have studied some numerical approach to linear algebra (like Strang's videos) first, rather than going straight into a book that's so abstract and proof-based.

I suppose it depends on your mathematical background.

(Your comment made me think about those folks who were once fit and muscular, then years later they are out of shape, and then they decide to get in shape say how easy it was to get back in shape. They don't realize that part of what made it easy is that they were once in shape, and they still more muscle cells or whatever.)

[resource0x]

Very true. But the same applies to teaching. Mathematicians don't know where even to begin - for some of them, it's all too obvious. But the same happens with any subject. Someone proposes a certain design - but after many (20... 30... 40) years in business, you feel the design won't ever work, and try to explain, and fail because you don't know where to begin.

[cgriswald]

I got a B in my linear algebra course which was basically only numerical. I’d have gotten an A but the professor thought mountains of homework was teaching and I refused to do it all. Suffice it to say I aced every test and all the homework I actually did. None of it helped in understanding and like the grandparent I remembered none of it at the end and turned to LADR.

I don’t think any of that numerical approach helped when I read LADR. LADR isn’t about “doing the work” it’s about “doing the work to understand”. Similar to your experience I remember reading the first chapter and then among the first chapter questions I saw questions that looked like they had no basis whatsoever in what I thought I had just learned. Then, eventually, it clicked. That’s, frankly, the only way it works with Axler, so if you want it, you’ve got to do it.

My advice is to not waste time with the numerical approach and just do it.

I had a professor who used to say “being a student is suffering” but he used it to justify a bunch of bullshit. In this case, though, I’d agree with him. LADR is suffering d followed by satisfaction (and rinse and repeat).