The Most Comprehensive Linear Algebra Book I Own

The Most Comprehensive Linear Algebra Book I Own

The book is "Linear Algebra by Friedberg, Insel, and Spence"

This is absolutely the most comprehensive linear algebra book that I have. I have used it as a reference numerous times! In this video I go over the pros and cons of this book.

(note this is my affiliate link, I earn a small percentage from qualifying purchases)

If you have any questions or comments please leave them in the comment section below. Thank you:)

[bluelagoon]

Learning from this book was an absolute struggle when I was taking linear algebra. As an analogy, it felt like the author rigorously proved to us how to do 1+ 0 = 1 and then expected us to to 3 * 5 in the exercises. I learned a lot more from my professor's and my TA's office hours than I did from the book itself.

[OleJoe]

You could add to your list the linear algebra books by Gilbert Strang. Also, "Matrix Analysis and Applied Linear Algebra" by Carl D. Meyer. For the "Jordan Normal Form", I've found that most books either don't cover it, or cover it superficially. I think the reason is that computer algorithms for the JNF are unstable and not recommend. The best book I've found so far for the JNF is "Matrix Operations" by Richard Bronson, in the "Schaum's Outlines".

[EpicMathTime]

Someone asked about this book in Wrath of Math's live chat last night.

This is one of the most underrated texts in math in my opinion. It is one of my favorites. I put in on the level of Dummit & Foote, easily.

As you said, it's extremely comprehensive. This textbook covered all of the material from my first undergraduate proof-based linear algebea course to my phd comprehensive exam on the subject.

The exercises are brilliant and creative, and are seemingly designed to strengthen intuition, which it does.

The book's writing style feels like a narrative through the development of the topic. It pulls you along as an active participant. It's not just "presenting" to you, it almost feels like you are an equal in the narrative, and are discovering and developing it with them. I truly adore this book.

[tauceti]

0:30 OOOH man those sections are juicy!
I gotta pick this up for sure.

[chaoticoli]

This is really a great book. I felt like it was the perfect difficulty for me because none of the proofs required too much ingenuity, but they did force you to really understand definitions and the connections between the theorems. Linear algebra seems to be like that in general. But now I am studying from Roman's text and I love it thus far, and it's a wonderful follow-up to this book.

[bm-brgo]

I'm a grad student and I reference this book just about every day. Absolutely mandatory for anyone going into pure math, especially functional analysis. The authors have a pretty clear bias towards analysts, which is great for me! It is my second favorite book on my shelf, next to Christopher Heils "A basis theory primer."

[peiopascualhernando]

It would be interesting if you made a video or video series about which math subjects you learned by yourself and what books you used for that!

[cybervigilante]

I've download a lot of the books you mention and I still don't know math.

What, you mean I have to study them? Damn.

[lamalamalex]

I absolutely loved this book. I sat down with it with pen and paper. If I had a tough proof, I did write it down following along with the author. Forced me to slow down and think and actually understand. I got so much better at writing proofs as a result.

[kristianwichmann]

Many moon ago, when I took my first uni course in linear algebra, we used Robert Messer's "Linear Algebra - Gateway to Mathematics" as a textbook. I have very fond memories of it, as it was really pedagogical in explaining the reasoning behind abstractions and so on.

[axisepsilon]

At my school, we have a linear algebra course for engineers and a linear algebra course for math majors. The latter course uses Fried, Insel, and Spence, and it is known to be a very notoriously difficult intermediate course at our school lol. About half the class drops out. Of those half who have survived, half of the people either get F or D, and less than 10 people receive an A in that course.

[ashishKjr]

I'm studying from this book and I've been enjoying it! I use Larry Smith's Linear Algebra as a reference. :)

[Alex]

This books is like the standard text of linear algebra courses for math major in my country. And it is considered the main reference for grad school entrance exams. Almost every math major in my country has this book!

[jackking]

I'm glad I watched this video - I was having daunting problems with it because I thought I had made progress learning linear algebra - I found a downloadable pdf copy of this book but just couldn't make it past a couple pages without feeling confused and daunted by the amount of work needed to get a deeper understanding.

I understand now I need to get a background in mathematical logic and proofs. Thank you.

[joeuwug]

A prof just recommended this book to me a couple of weeks ago, and I enjoy it!

[rontiemens]

Just got my copy from thriftbooks! I agree about the rigor and robustness of this book. An excellent part of any library of anyone interested in math.

[pinklady]

Now, I am viewing books on linear algebra before ordering copies online. Great review.

[ianmii]

Cool! During my college years I possessed the linear algebra textbook by Richard Hill, similar content. Some time after I sold it because I was needing some money at that time.

[listsforthecurious]

A great exposition of the pure mathematics behind Linear Algebra is the MMA's "A Guide to Advanced Linear Algebra", by Steven Weintraub. It is written in a standard Theorem, Lemma, Proof format, without any excercises, so it isn't much good for studying for a Linear Algebra exam, but it lays out the proofs of all of the results very nicely, so it is great if you want to understand Linear Algebra with an eye to original research or from the perspective of wanting to write proofs.

[rodrigodiazarancibia]

Excellent book! I'm studying for my final test with it. I feel more solid, and the exercises have progressive difficulty so feels nice to do all the exercises.