I've been studying Linear Algebra and Matrices for fucking years now but I honestly understand absolutely nothing thanks to my mental disability. What's the best textbook that teaches all the concepts with real-life examples and their implementation?>inb4 just give upI can't give up, I need this job.As many solved examples as possible. Thanks.I need to solve the questions pen and paper so no coding shit.
Linear Algebra and Its Applications by David Lay is probably a good fit
>>16847356>Ok, I get numbers alright>What's this? A symbol representing arbitrary numbers?Hm alright>Oh no, who put them in fucking squares?
>>16847356A job from solving linear algebra questions on paper?No such thing.
>>16847356Nobody wants to hire someone who does something as basic as linear algebra
>>16847356 (OP)1. A First Course in Linear Algebra by Edna Kramer2. Introduction to Linear and Matrix Algebra by Nathaniel Johnston3. Linear Algebra: A Modern Introduction by PooleTry these. And remember to drill stuff at all stages.>>16847376OP probably runs into the same issue lots of people run into, where the text complete skips over the jump between algebra and linear algebra. Matrices are never explained as the shorthand that they are. They're just treated as fundamental objects with a set of weird procedures, explained (if at all) in jargon-heavy nonsense that people have no grounding for. Most people already have a grounding in basic algebra, but just throwing them into the deep end with unfamiliar representations on top of having to learn the why/how basics is unambiguously dogshit pedagogical practice. For some reason it continues to persist, but I have seen it time and again that if you aren't so retarded with pacing you get much greater success. People struggling with matrices no longer struggle when you start them off doing things the verbose way, get their intuition built up, and then start introducing the magic shorthand shit.It's like trying to teach basic algebra to someone that's unfamiliar with arithmetic. >Don't worry about what the "+" and "*" mean, they're manipulated this way because of the commutative and associative properties as they apply to the sum and product operations in our ringLike you really think that's a fucking start? Because that's how Linear Algebra is taught.
>>16847356>the best textbookthe best textbook is one that has an application you care about that utilizes linear algebrai suggest graphics, which will exercise your geometric intuition to the point where the definitions are hammered into your head, which allows you to think about more abstract spaces (such as higher dimensional, both countable and uncountable)
>>16847827Teaching math wrong so retards don't get it is based. They're supposed to get confused and quit.If you're smart, you can learn even if you're taught wrong.
>>16847895based and true
>>16847895>Teaching math wrong so retards don't get itThe thing is, that's not even teaching it wrong. The correct way to teach math is in such a way that retards get automatically filtered out. It is the attempts to make math "accessible" which are problematic.
>>16847356The easiest Linear Algebra book I've found is "Linear Algebra: Step by Step" by Singh. The book has brief solutions at the back and full solutions (including full proofs for the proof questions) on the Oxford University Press website.
>>16849436>Singh
>>16849534I don't care if he's Indian. He's taught Real Analysis, Number Theory and Linear Algebra at the University of Hertfordshire in England for 20 years. His book is good is as easy as Linear Algebra (with proofs) gets. Picking books based on the author's ethnicity instead of its contents is peak tard behavior.
>>16847356I highly, HIGHLY recommend Gaitsgory's notes on Algebra I (Math 122) and Algebra II (Math 123). They lay out the theory clearly, what matrices actually are, what linear transformations are, etc. Most books have no clear distinction between application and theory and end up presenting those concepts in a really confused matter. You shouldn't have to do a full course on group theory and commutative algebra before seeing a single vector space but clearing up what those structures are before moving on to more complex structures like a vector space helps a lot with getting used to the formalism.Also, it's just notes and thus doesn't have many examples, but I still highly recommend you read through them as a lucid treatment on just the theory, feel free to supplement other texts for exercises and examples (the notes actually have exercises too with solutions to a lot of them but they're not really focused on computational stuff).
>>16850486>OP can't into the basics of the simplest algebraic structure>Let's recommend Gaitsgory's noteskek
>>16850520nta, Gaitsgory is insane for doing full-on representation theory in a first-semester Linear Algebra course (actually, all his courses cover way too much fucking stuff) but it's the right perspective in the sense that if you want to become a great mathematician/work alongside leading researchers, you need to know a fuck-ton, much more than is usually covered in courses (save for his, maybe). A prof once told me Gaitsgory apparently studied homological algebra in HS and it shows lol.
>>16850480I do care he’s a pajeet. It’s not like we lack linear algebra texts at any level.
>>16847356A matrix is some sort of rule (like a function) that transforms an input vector (a list of numbers) to an output vector. That's it. All of the theory is gay and useless for engineering.
>>16847356Use chatgpt and tell it to generate problem sets for you to drill with and provide explanations when you get stuck.
>>16847895>teaching math wrong so retards dont get itThis is why the best thing to tell people like OP is to use chatgpt.
>>16850520if you're a code monkey yeah just drill matrices for a week until they're burned in. but if you actually care about doing more than just retard slave work, that's not gonna cut it.
>>16847897based
>>16850520Yeah? It's not like it's going to get any easier if you keep on reading "LinAlg for dummies"-type books
>>16853276wrong, but it's not like you'll engineer anything impressive in your lifetime anyway
>>16850486seconding them>>16850520fucking retard
>>16847356Check out Gorodentsev's "Algebra I". It's a fairly comprehensive Linear Algebra book in everything but the name (see pic rel, later chapters cover modules, bilinear forms, etc.)
>>16847356Just read strang if you care about applications or lang if you will never have to take transport phenomena and resistance of materials in your life
>>16855482>You're a retard for thinking that an anon who can't into vector spaces should be reading GaitsgoryOkay
>>16855846yes, you are, actually read the notes. There's nothing in them that's too advanced, they introduce everything starting with semigroups. They don't even treat shit like modules in an advanced manner like you'd see in a commutative algebra course, it's really just a matter of presenting the material surrounding linear algebra in a clear manner. I'd say these notes are pretty much a standard 2-semester linear algebra course save for rep theory and the commutative algebra stuff near the end
>>16855884OP is not going to / trying to become an adept mathematician. You've evidently not tried to teach people like him. They are literally incapable of grasping definitions. You tell them what is a semigroup, monoid, group in week 1, and in the subsequent 14 weeks, they will be completely lost at their mention.
>>16850520>>16855846>>16855884>>16856021I've a learning disability frensalso let the thread die now
>>16847356What other uses does LA have? I was only taught to solve differential equations with it.
>>16857348They underlie pretty much anything you wish to do in math.In representation theory, you study groups via their actions on vector spaces.Any time you want to talk about infinitesimal behavior, you're going to be talking about a linear structure, so it always appears in geometry. Using this idea, since inner products, norms, seminorms geometric structure on vector spaces, they may then be used to give such structures to your geometric space.As you mentioned, they're used in differential equations; more generally, functional analysis is the study of topological vector spaces (i.e. vector spaces with additional topological structure).Vector spaces also behave very rigidly, and in a precise sense have an algebraic structure with nice properties. A good deal of algebra (and dually, geometry) studies algebraic structures with deviations from these properties.I'm pretty sure there are various combinatorics (hence graph theory) problems which can be solved using linear algebra results applied to vector spaces over finite fields.A better question is if there exist any areas of math which don't have any relation to linear algebra (the answer is probably no).
>>16856022You're the only one putting yourself down. Have some self-respect
>>16847356I'm currently working out of this book, teaching myself linalg on my own free time.https://theportal.wiki/wiki/Linear_Algebra_(Book)
>>16847356cast 5 spells to understand and do linear algebra
>>16847356VMLS is the best applied linalg book and its free, you mainly do modeling with ithttps://web.stanford.edu/~boyd/vmls/
>>16856022no
>>16847356I had a kind of shitty undergrad (physics and math) where my intuition for lin alg was built around its applications in quantum. I found Axler most helpful for uniting the ideas I encountered in group theory and analysis with that intuition, but it really is a book you should understand sooner rather than later.I did find Axler to be among the easiest books I've read through, though.What exactly are you struggling with?
>>16847365I second thisOne of the textbooks I liked the most
