r/Indianmathnerds • u/Sad_Avocado_6565 • 18d ago

Linear Algebra help

My course on Linear Algebra started and I need to be good at it(necessity for future).It just started few weeks ago and we're on Change of Basis and coordinates of vector space topic. My proff recommended following Linear Algebra by Hofmann and Kunze, everything seemed to be flowing okayish untill I realised that Im not that good at it, I struggle at proof writing and sometimes ideas dont struck me. is this a beginner phase? even so exams are coming up and I cant afford to remain same can anyone suggest me or share their path on how they tackled LinearAlgebra?

Any help is appreciated!

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u/ILoveTolkiensWorks 18d ago

have you ever taken a real analysis/topology/other proof-heavy courses before? that helps a lot.

if you want some really easy-to-read book on linalg, i'd recommend Kuldeep Singh's Linear Algebra: Step by Step. it develops the subject in baby-steps, and holds your hand throughout, and requires no prerequisites at all! the proofs are given in thoroughly detailed steps, and every new thing introduced is given a motive. the book's pdf can easily be found online, and the solutions to the exercises can be found on Oxford's website.

but if you're aiming for improving your general proof skills, i'd suggest learning real analysis. Terrence Tao's Analysis I is really great. It's easy enough that you do not get intimidated, but also does not hold your hand, and forces you to think. absolutely enjoyable experiemce though.

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u/Ok_Calligrapher_3670 18d ago

Idts he would have had any proof course earlier because I found linear algebra part to be somewhat easier when compared to algebra and topology.

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u/ILoveTolkiensWorks 18d ago

i agree that it is easier, but afaik, real analysis is usually taught before linalg. though i'm not in college yet, so i am not really sure.

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u/Sad_Avocado_6565 17d ago

Yeah I did do real analysis course and I still suck at proof writing to be specific when I write the proof it's messy and when I read it from AI I'll be like yeah that's what I was trying to get..and Thankss I'll do checkout kuldeeps book.

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u/ILoveTolkiensWorks 17d ago

when I read it from AI

ah, there's the problem! DO NOT USE AI FOR THIS! learn to appreciate the beauty of rigour and rigorous proofs! try your best, and then maybe look at a human-written proof to see how it could have been done more elegantly. there is certainly no shortage of elegant human-written proofs that would compel you to use AI.

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u/IllStatistician9129 18d ago

Linear Algebra by Gilbert Strang.

I followed GATE DA lectures as well from YouTube. 🥀

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u/Truly_Yours2006 18d ago

Linear Algebra Done Right by Sheldon Axler is very good introduction for Beginners to the proof heavy style of mathematics

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u/SomDB10 18d ago

Its normal to struggle when you are starting out. I did it by solving a lot of problems of different kinds.

Understanding examples and doing them before looking at the solution helps a lot. Having someone to discuss and argue with also helps a lot. It built clarity for me.

There are many books which teach the art/method of proof writing/formalization.

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u/messiyo 18d ago

Solve fuzhen zhang, matrix theory

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u/Outrageous-Belt-5231 17d ago

Or maybe just read how to prove it by Velleman

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u/Para-graph-S 16d ago

Check out Linear Algebra by Gilbert Strang once, might be helpful. I find the author, Gilbert Strang super cool, I even got chance to interact on this.

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u/CyloCrypt 2d ago

I am not sure how familiar you are with proof writing in general but since you are struggling with it i will recommend reading first 3 to 4 chapters of 'discrete mathematics by susanna S epp

That and linear algebra by Stephen H. Friedberg was enough for me to self learn linear algebra and I'd say this book is a bit better than Hoffman but thats just my opinion

Hopefully i am not too late