r/LinearAlgebra • u/Illustrious_Past_621 • 1d ago

Looking for proofs based LinAlg textbook.

Hey all, my dual enrollment course uses Gilbert Strangs Introduction to Linear Algebra 6th Edition, however I'm kinda frustrated with the emphasis on computation rather than understanding. I went through a decent chunk of LADR but I'm finding it hard to keep track of what I'm "meant" to be learning for class, so I was wondering if anyone had a recommendation that followed the content of Strang, but had a larger emphasis on proofs.

Also, does anyone now of any good books on ODE's?

11 Upvotes

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4

u/somanyquestions32 1d ago

Get the books from Otto Bretscher and Friedberg, Insel, and Spence.

For ODE's, I liked Boyce and DiPrima.

1

u/Midwest-Dude 1d ago edited 1d ago

I agree with Bretscher, close match to Strang's layout. Boyce is good, never touched DiPrima. Edit: Oops ... didn't realize they coauthored ...

2

u/somanyquestions32 1d ago

Boyce and DiPrima are co-authors for the same elementary differential equations textbook.

1

u/Midwest-Dude 1d ago

Aha! Thanks!

1

u/somanyquestions32 1d ago

My pleasure! 😄

3

u/Midwest-Dude 1d ago

A search came up with these suggested resources:

  1. Linear Algebra

    • By Jim Hefferon
    • Free Resource
    • Closely follows Strang's entry point with systems of linear equations and Gaussian elimination, while introducing rigorous proofs and providing complete, step-by-step solutions to every single exercise in a dedicated answers manual.

  2. Linear Algebra: A Geometric Approach

    • By Ted Shifrin and Malcolm Adams
    • Paid Resource (Used, typically start ~$15–$45 on ThriftBooks, compared to $200+ new)
    • Mirrors Strang's chapter outline and geometric focus beat-for-beat (including the four fundamental subspaces and projections) while elevating the material to a rigorous, proof-based undergraduate level.

2

u/CactiWasHere 1d ago

i really liked linear algebra done wrong by sergei, amazing book really

4

u/jphamlore 1d ago

Linear Algebra Done Right by Sheldon Axler

https://linear.axler.net/

3

u/username_is_alread- 1d ago

I think OP already mentioned going through a decent chunk of LADR and was looking for alternatives with coverage closer to that of Strang, just more proof-based

2

u/Midwest-Dude 1d ago edited 1d ago

This is a poor match to Strang, as the OP states. Axler aggressively delays matrices and completely restructures the learning path, so trying to keep pace with Strang would be difficult at best. As the Redditor notes, it makes it very difficult to map what you are reading to what the professor is lecturing.

2

u/BrightScarlet 1d ago

How about "Linear Algebra" Friedberg-Insel-Spence

2

u/jphamlore 1d ago

This looks reasonable. It also has a freely available student solution manual.

Trench, William F., "Elementary Differential Equations with Boundary Value Problems" (2013). Textbooks Collection. 8.

https://digitalcommons.usf.edu/oa_textbooks/8

1

u/Thermite365 1d ago

Abstract Linear Algebra by Curtis. A really fun one is "Linear and Geometric Algebra" by Allan McDonald.

1

u/SnooHamsters6536 22h ago

I have some Lectures Notes on Linear Algebra by Terrence Tao. Really like his approach and proofs.

1

u/DifferentialOper8r 19h ago

I like Lang’s books a lot

1

u/nsmon 11h ago

Apostol's calculus vol. 1 has a decent chapter on linear ODEs and vol. 2 a not terrible couple of chapters on linear algebra

1

u/Additional_Yogurt888 1d ago

Just use the textbook your professor recommends and focus on getting top marks in the class bro, you'll learn more theory from your advanced classes like linear algebra 2 and on.

2

u/Illustrious_Past_621 1d ago

I'm addicted to math, I just need ODE and I have my Mathematics associates in 11th grade.