Linear Algebra is Impossible Without These 8 Things

📊 Do you need PRIVATE CLASSES on Math & Physics, or do you know somebody who does? I might be helpful! My personal Whatsapp and email: [phone] ; [e-mail]
📈 Check out my Udemy courses (you may find something that interests you 😉): www.udemy.com/user/luca-di-beo/
🥹 Consider supporting us on Patreon:
www.patreon.com/user?u=86646021
😎 Become a member to have exclusive access:
/ @dibeos
_______________________________________________________
📊 Linear Algebra is the cornerstone of modern mathematics, shaping subjects from quantum mechanics to computer graphics. 🌟 Join us as we delve into the top 8 discoveries that have profoundly influenced this fascinating field.
Journey back to the origins of linear algebra, where ancient cultures like the Chinese pioneered systems of linear equations, leading to groundbreaking solutions beyond simple graphing. 📜 We'll explore how the Nine Chapters on Mathematical Art and early problem-solving methods paved the way for further advancements.
Fast-forward to the 1800s, when Carl Friedrich Gauss transformed how we understand linear equations through Gaussian Elimination, laying the groundwork for modern matrix theory. Dive deep into matrices, their history, and their pivotal role in solving linear systems. 🧩
Determinants & Cramer's Rule: Explore the properties of determinants and their role in solving systems of equations, influenced by Gabriel Cramer and formalized further by
Laplace and Cauchy. Understand how determinants ensure that linear equations have unique solutions, crucial in complex scenarios. 🧮
Vector Spaces & Linear Transformations: Uncover the mysteries of vector spaces, as pioneers like Emmy Noether and Emil Artin expanded our understanding of higher dimensions. 🛤️ Learn how linear transformations map vectors in space, giving structure and meaning to changes within vector spaces.
Eigenvalues, Eigenvectors, & Inner Product Spaces: Discover how James Joseph Sylvester and David Hilbert revealed the power of eigenvalues and eigenvectors to decode matrix transformations. Then, delve into inner product spaces, thanks to John von Neumann's insights, understanding orthogonality, norms, and the geometry of vectors.
🚀 Explore the Evolution: Finally, see how these cumulative insights evolved linear algebra into the field we know today, directly impacting areas like quantum mechanics and beyond. Whether you're a math enthusiast or just curious, this video is your ultimate guide to linear algebra's fascinating history and its pivotal discoveries.
#LinearAlgebra #Mathematics #Algebra #QuantumMechanics #MathHistory #GaussianElimination #Eigenvalues #Matrices #LinearTransformations #VectorSpaces #MathEducation #AdvancedMath #Determinants #MathDiscoveries #Gauss #Cramer #Cayley #Sylvester #Vectors #InnerProductSpaces #OrthogonalVectors #Orthogonality #Orthogonalization #MathTheory #ScientificHistory #MathGeniuses #MathTopics #STEM #LinearEquations #MathTutorial #MathLecture #Eigenvectors #DotProduct #AdvancedMathematics #MathResearch #LearningMath #MathExplained #AlgebraLearning #MatrixMath #VectorMath #ScienceEducation #MathEvolution #MathDevelopment #InspirationMath #MathJourney #ModernMath #MathConcepts #VectorCalculus #STEMEducation #MathVideo

[@fromant65]

The linear algebra lore is quite easier to understand than the gameplay

[@MattHudsonAtx]

I gave up on gameplay but I still follow all the best cheat tutorials

[@aniksamiurrahman6365]

"Unfortunately, no one can be told what the Matrix is. You have to see it for yourself." I couldn't hold myself from this. LOL!

[@dibeos]

Morpheus was a skilled mathematician.

[@antoniusnies-komponistpian2172]

An mxn-Matrix over a field K is a mapping from {1,...,m}x{1,...,n} to K. How about that?

[@dibeos]

@@antoniusnies-komponistpian2172 yep, you outsmarted Morpheus 👏🏻😎

[@koromi2999]

Its awesome to hear how things were developed, that helps a lot in uderstanding certain topics

[@dibeos]

Great! We are glad you liked it. Let us know any other subject (related to math and physics) that would be helpful to understand how it was developed 😎

[@danielc.martin1574]

The origin of the name "matrix" was actually given by Sylverter to refer to what a determinant takes. That is, a matrix was something that was the matrix of a determinant. The name determinant I thing is obvious

[@deepaka.v2971]

Highly informative ✨️ Q and A format is effective

[@dibeos]

Thanks man!!!

[@jean-marclugrin1902]

Nice video, thanks. May I sugges that yo uenhance the sound quality of the speakers ? Better microphone, clip microphone and/or room with less echo ?

[@dibeos]

Yes!!! You are right. We need to think about a way to eliminate the echo… the mic we bought is really good, but we still don’t know how to create the right environment in order to do that. Do you have any suggestions?

[@godhell8039]

Awesome!👏 Luca, complimenti vivissimi ad entrambi! Due domande: 1) Non caricherai più video sul canale in lingua italiana? 2) Anche la tua compagna è matematica?

[@dibeos]

Ciao! Vogliamo tantissimo farlo però abbiamo capito che cercare di fare video in tutti e due è troppo pesante… quindi la nuova strategia è concentrarci su questo qua e crescere questo canale visto che il pubblico è più vasto. Infatti, abbiamo monetizzato proprio oggi il canale! Haha quindi useremo questi soldi per pagare qualcuno per fare l’editing, così abbiamo più tempo per produrre più video. Non sappiamo esattamente quando, ma appena vediamo che il canale ha una dimensione abbastanza grande, cominceremo a caricare video in quello in italiano pure. Purtroppo, non si può avere tutto contemporaneamente 😣. Per quanto riguarda Sofia, lei è laureata in storia, ma comunque trova la matematica e la fisica molto interessanti 🙂‍↕️ ma lei è bravissima sopratutto facendo tutte le animazioni e lo script. Insomma, diciamo che io ho la conoscenza tecnica e lei la conoscenza artistica haha

[@Resultofhours]

Your video quality is just awesome 👌

[@dibeos]

Thank you for the nice words! 😎

[@scottychen2397]

To the lady speaking, Hold on, and No: an ammonia molecule’s geometry has nothing to do with the concept of eigenstates. - despite the first treatment of it, theoretically. That’s why Feynman understood that shit well. There’s seriously a pressure in his global understanding of it to be having correct concepts. It’s initially distinctly incorrect. That’s acknowledged far after chapter 9 of the QM-red book. If you can’t see the need, Then this Linear Algebra is healthy for you. For it now lies in potential that you will grasp the distinction.

[@alifrahman7099]

Good stuff man!

[@dibeos]

Thanks man 😎

[@ifrazali3052]

Beautiful video as Always

[@dibeos]

Thank you Ali, and you giving us a nice comment, as always

[@hardwork3199]

it s been a while since i watched you videos but they are great as always

[@ashutoshsahu654]

I think u should cover the calculus war which held betwn Leibniz and Newton for calculus for better understanding of its use..

[@dibeos]

Yeah, I have a video about it, but it is not too deep on their conflict. Let me know if it is useful 😎

[@ashutoshsahu654]

Yes....my favorite teacher

[@ashutoshsahu654]

I want ur wp number to clear about my some doubt

[@Konstantinoff74]

Excellent video

[@dibeos]

Thank you! What did you like about it? Did you learn something new? 😎

[@AhmedYasser-33843]

Keep going, man. This is beautiful🌹

[@dibeos]

Thanks Ahmed!! Let me know what you liked about it and what would want to see in the channel 😎

[@AhmedYasser-33843]

@@dibeos I hope you dive more into the concepts.

[@ashutoshsahu654]

Your vdo about Development of calculus was so much useful for me becoz as a mathemaric student we have been just given so much integration to do without knowing the real necessity of it. I really harashed becoz i don't know why i am doing this maths. But later i came across with ur vdo and my doubt were gone. Now i'm not a machine but machine who know the mechanism....

[@dibeos]

Great comment. I think it is really easy to just calculate things without understanding the big picture. Keep it in mind

[@toastyug]

Good thumbnail and title!

[@dibeos]

Thank you, Toasty!!! 😎🤙🏻

[@rileythesword]

Nice video, I studied linear algebra but it was mostly more mathematic than visual so I appreciate this more visual element of the video. ❤

[@dibeos]

That’s awesome! I’m happy it was helpful. Are there other subjects that you’d like to learn in a more “visual” way?

[@rileythesword]

@@dibeos I’m thinking topology maybe if that’s something you have experience with, mainly visualize mapping functions similar to the transformation in this video!

[@dibeos]

@@rileythesword oh yeah! My masters thesis was about an area of topology. I will add it to the list, thanks 😎

[@rileythesword]

@@dibeos okay then, awesome!👍🏻

[@NaN_000]

Nice video

[@dibeos]

Thanks NaNaNa… I appreciate it 😎

[@hardwork3199]

4:42 , so what are they ?😅 can we imagine them ?

[@dibeos]

Good question. Vector is a mathematical concept, and therefore it requires a mathematical (rigorous) definition. However, vectors are soooo useful in physics that physicists adopted them almost as if it were an inherently physical concept. In physics, as far as we know, there are only 4 dimensions, so it doesn’t make sense to treat vectors in physics using its most powerful and complete (but also more abstract) mathematical definition. Basically in physics it is enough to imagine a vector as an arrow. The correct rigorous definition would be: an element of a Vector Space. So then one asks: what is a Vector Space? It is a set of mathematical objects equipped with addition, and scalar multiplication, such that these operations satisfy: associativity of addition, commutativity of addition, etc… (it is easy to look up the entire definition). So basically, not only arrows satisfy these conditions. Some functions, “n-dimensional arrows”, polynomials, matrices, sequences, tensors, differential forms (etc) are all examples of vectors, by this rigorous mathematical definition. Is that clear? 😬

[@hardwork3199]

@@dibeos yes , thank u

[@bhaavaniidasa2651]

I heard you have a white Elantra for sale

[@dibeos]

Really? Even I didn’t know that 😅😂

[@byronwilliams7977]

This was fun

[@dibeos]

Thanks, Byron!! 😎🤙🏻

[@craigkdillon]

And here I thought all you needed was lines and algebra. Silly me.

[@dibeos]

Hahaha yeah, linear algebra (and analytical geometry) can give this impression 😎📈

[@xyz-bo1mr]

This channel is gonna be famous soon

[@dibeos]

Thanks, really!! We just hope to grow as soon as possible and literally reinvest all the money it makes into the channel (and also expand in other languages in the future) so that we can produce more and better videos 😎

[@xyz-bo1mr]

@@dibeos you will

[@princeplayz8374]

don't stop uploading

[@dibeos]

We won’t!!! 😎 but why do you say so? (Curiosity)

[@hardwork3199]

@@dibeos because humans love learning new things especially in domains we like , and seeing you guys not having enough support makes us afraid that you will stop :,(

[@dibeos]

@@hardwork3199 wow that’s an awesome comment. Thank you for the support 😁 we won’t stop at all, this is just the beginning 😎

[@ccuuttww]

I think 99.999% of the time is about projection

[@dibeos]

It is indeed 😎

[@geoffreyfaust3443]

You want to pronounce it 'or-tho- NOR'-mal'. I know, Englsh is weird.

[@dibeos]

Got it! Thanks, in the next videos I’ll say orthoNORmal 😉👌🏻

[@scottychen2397]

If you think the linear algebra in special relativity has anything to do with the concept of relativity (special or otherwise) You did well calling this linear algebra. And not anything else. Because that shit isn’t relativity, except when you understand the underground shit. Which I can already see you don’t. So you’re sitting and speaking in my territory, if you think you understand a thing about relativity with this shit. 🦝 Is it quantum mechanics? It’s not the world view; but it’s the vocabulary. (1) the worldview: an ontological status vibration of entities (Sydney Deng) is read from the collected data that is of a statistical nature (2) concept of a basis: is the only the part of the linear algebra that isn’t properly outside the essential quantum mechanics - and exists as ‘embedded’ in the quantum mechanical worldview in the modality of ‘example’ to supply the continuously-conceived-from-a priori worldview , the equating between ontological vibration and statistical data. Implying….. perhaps other means of embedding. The result of the logic in the practical sense which enjoys the illogical: ‘Rho is mod psi squared’ : a feature I don’t believe is a priori logical even with experiments to ‘suggest’ it: for this is where one reads mechanics from statistical data: psi from rho. 🦮now, I’m not saying that Fermi doesn’t know what he’s talking about. But this is the only thing that’s unacceptable. It’s pure theoretically understood as coming out of thin air - especially with a non-understanding of the abstract probability space. The de-broglie particle is sensible. And the schrodinger equation comes pure Logically from this. The problem is the untestability of worldview that has an open sense of mechanics. The difficulty therefore is having a singular concentration on the potential data that psi (not rho) implies. (Mod psi)^2 = rho, Therefore, is the only thing that’s truly (1) Einstein: incomplete as a worldview (2) Fermi: unacceptable as it exists in a working-theory (3) Schrödinger: made up, in reference to the cat’s eigenstates as a test to this theory’s rigor (4) Heisenberg: reason to interpret any such dispersive data as evidence of unknowability as a pure metaphysical deduction. (Unknowability a priori doesn’t necessarily follow from probabilistic knowledge) (6) Feynman: not something that will ever be nakedly seen in rigorous scrutiny for the empirical system he specialized in. - the ammonia maser. In particular, one is mostly studying an entity that can have two different energy states…. That’s about it! (7) Von Neumann: a reason to devote his life to building mathematical extraneaities…. Which could itself be understood as an experiment to see which mathematical entities will get ‘distilled’ as a study that is richly studyable for a diversity of personalities e.g. there’s many ways of conceiving of the iterated same-type event that will have been exacted and seriously believed in way….. i’m suggesting that there’s many ‘mechanics’ then, that a formalism would imply…. which is not necessarily a problem; however it demands the question of exactly what mechanics: The blinking in out of existence here means potentially too many things to be considered ‘understood’ in the sense of mechanics. The blinking in and out is first concieved of with the linear algebra (consider an orthonormal system that is algebraically 2 dimentional) The concept of even the existence of an alterior orthonormal system is now seen as Extremely powerful as in the case of modeling an ammonia maser. This is the beginning of conception of ‘quantum mechanics’: And the concept of de-broglie wave completes the gap between (1) the general varying between two (or infinity in the case of using a hilbert state space) states of being. and (2) the mechanics by which an entity would continuously transform into a nonpercievable field of probability density, which can be experientially percieved as distinct states of being. This linear algebra has nothing to do with the linear algebra one uses in the study of lorenz invariance, and the concept of relativity can be used pure theoretically to grasp the nature of mechanics implied by the de- broglie wave. In particular, what experimental reality would a quantum state appear as? e.g. The classical concept of force and how that exists here once again seems relatively independent of the canonical analysis, until one has collected all the point particles into one mathematical entity: The walls that an entity perceives as appearance around one at all times is primarily a potential well. As something that is not physical, and perhaps not intrinsically a feature of the concrete/paint/other materials that are classically responsible for exercising a fundamental potential energy that is found in the bulk psychological.

[@hardwork3199]

😮 😮 😮 😮 😮 😮 😮 ok i ll try reading the first lines , if im hooked i ll read it all

[@hardwork3199]

nvm , im still young for this ""shit"" as you said 😒