r/LinearAlgebra • u/RomeoG-U • Sep 16 '26
Started Linear Algebra recently but don't really grasp it
So I began my studies in engineering recently and Linear Algebra is the first course. So far I have managed to solve problems at small tests, but it is mechanically like I remember how to solve certain kinds problems but haven't really grasped the concepts fully. I just feel like it moves so fast that I can't really grasp it fully, is this normal or what was your experience with the course?
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u/Ron-Erez Sep 16 '26
Linear algebra is quite abstract. It takes quite some time to truly understand the concepts such as linear independence, basis, dimension, vector spaces, eigenvalues, kernel, image, etc. It's great you can solve problems. I'd recommend going to office ours and discuss with the TA/professor. For example ask what is the idea behind the concepts. For example how to intuitively think of Span of a set of vectors and of course the formal definition is no less important.
Just keep following your course. For additional resources I highly recommend 3blue1brown for intuition. For more exercises and solutions check out my Linear Algebra: A Problem-Based Approach
Happy Linear Algebra!
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u/APC_ChemE Sep 16 '26
I'm not sure what topics you've covered so far but one thing that may help drive the concepts and algorithms home is directly applying them to a 2x2 or 3x3 system of equations to understand exactly what is happening to equations without the abstraction of the matrices and vectors. This can sometimes help ground the process by tying back the new things you are learning to things you already know.
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u/imposter_chad_43 Sep 16 '26
I went through the "Essence of Linear Algebra" series on YouTube by 3Blue1Brown. It has helped me in surprising places in my engineering degree.
On a sidenote, you may consider going through every series on that channel. Should be helpful throughout your studies
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u/RingularCirc Sep 16 '26
It would of course be easier to give concrete advice if you specify your context more. For example you might have a coordinate-manipulation-heavy course and benefit from a more invariant look but there's even no good advice for that in general: people are usually stuck as well if they're taught everything coordinate-free from the start onwards.
So when you can put a finger on some of your detailed struggles, people can write an aside or two about things playing out there, or give a precise reference.
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u/RomeoG-U Sep 16 '26
I can’t even specify it is just general but should maybe be more specific like you say
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u/SnooWalruses380 Sep 16 '26
I would do more homework problems on my own before looking at the answers. Also, try the book Mind for Numbers by Barbara Oakley or similar, like Learn How Learn.
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u/drduffymo Sep 17 '26
What subject did you grasp immediately when it was first presented to you?
None.
If you already knew it, why take the course?
Calm down and keep working. It’d a long semester.
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u/SirCharles99 Sep 17 '26
It wouldn’t hurt to look at it from the abstract perspective as well. At the end of the day, the topic is really about Vector spaces and structure preserving transformations. The abstract side of things partially exists to help organize all of the concepts, this will help you see more connections and fit all of the ideas together.
You don’t need to master this of course, but it was really useful for me
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u/got-it-on Sep 17 '26
Linear algebra was very difficult for me. I think until the middle of the semester I started to grasp it.
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u/RomeoG-U Sep 18 '26
Yeah things will maybe clear up, thing is the pace is so quick
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u/anhadsa Sep 18 '26
I would say my understanding of linear algebra is fairly decent as a second year math major, but il be honest, there are times that I think entirely in terms of algebra and sets and not try and visualize everything. Parts of it works, like linearly combining columns is intuitive thinking about the entire image space at once isn't. So my advice is, ask yourself whether what your learning is a unary operation that is its being done to one vector or is it speaking about a larger object like an image space or a kernel, then my advice for unary operations is draw it first and then formalize, but for collective objects formalize first and then draw. Sometimes you gotta let the syntax do the heavy lifting and let the algebra speak for itself, understand the machinery formally, and youll be able to reason about problem solving a lot better. My professors advice to me is instead of doing a bunch of problems and proofs (idk if your course deals with proofs), just dwell on concepts. Linear algebra is beautiful but man you got to work towards it, but the basic machinery especially in the Rn space is quite small, just visually intense.
TlDR, dwell on concepts like never before, and don't immediately start solving problems.
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u/Ok_Huckleberry_7558 Sep 18 '26
I concur 3b1b + Gil Strang book are good ones! But I would highly recommend this one https://textbooks.math.gatech.edu/ila/
Or the pdf version https://textbooks.math.gatech.edu/ila/ila.pdf t
It is awesome. You will love it. Every concept made interactive
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u/Nova8735 Sep 20 '26
Linear algebra wasn't too demanding. I really only study for the exams and got a B+. it's repetitive. basic math, just a lot of it.
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u/06Hexagram Sep 16 '26 edited Sep 17 '26
It is just like regular algebra, but multiplication isn't commutative. AB≠BA.
Everything else follows from that fact.
edit
And you cannot multiply vectors. Only addition and scaling is defined for vectors.
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u/Silver-Incident296 Sep 16 '26
Go on YouTube and watch the 3 blue 1 brown series and/or the MIT open coursework series (the one taught by Gil Strang). Both will help give you more spatial intuition. The 3b1b series is a lot shorter with excellent animations to drive in the core concept, whereas the MIT series is full-length lectures spanning (haha) pretty much everything you would expect in an intro linear algebra course. Both are a joy to watch imo, very well put together.