Matrices: Why they even exist?
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- Опубліковано 20 чер 2024
- A brief coverage of the history of matrices from the point of view of Engineering Maths.
There have been so many mathematicians involved in the development of matrices, I've only named a few in this video that I feel contributed heavily to what you're exposed to in engineering maths.
My resources for the information:
1) Absolutely brilliant resource for a timeline of information regarding the history of matrices ... www-groups.dcs.st-and.ac.uk/~h...
2) Around pages 177 and 515 in A History of Mathematics by Carl B. Boyer and Uta C. Merzbach. A great book covering the history of mathematics, you can pick up a copy on Amazon here: amzn.to/2PNO3z0
Intro music by an amazing band called Wordy, check them out here:
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Maths history is very important helps us understand the concept faster and better and helps kind of know why we are even studying it in the first place
I couldn't agree more David.
@@ciaranmcevoy9875 why sir
Well said👏🏽👏🏽
I agree 💯%
History, in general, is greatly undervalued!! History helps all of us connect the dots.
I just discovered that knowing all about the history of matrices makes me learn matrices much better.
the fact that you arent reading a script, or at least practised the damn thing and memorised, helps me listen. great vibes man! underrated channel
Thanks pal!! Really appreciate the recognition of the effort!
It's worth adding that matrices were still quite an obscure topic even in the 1920's. Heisenberg's use of matrices in quantum mechanics did a lot to popularise them.
Nice! That is worth adding, I didn't know that. It seems funny that quantum mechanics would be the topic that popularised them further. Not exactly the most approachable topic 😂
@@ciaranmcevoy9875 Popularised I think in the sense that they were seen to have a real world application - and remember things such as gaussian elimination, determinants etc. were largely taught and understood notationally as part of algebra - and so many working physicists started adding them to their working knowledge, and thus ended up in syllabuses further down. General Relativity and tensor algebra that came from it was probably another impulse. After they started being used more in cutting-edge physics and appearing on standard syllabuses the engineers then started using them as a tool to simplify calculations around things such as vibration analysis and stress tensors. The maths syllabus at a lower level is obviously quite conservative, but I would say linear algebra has slowly replaced a lot of technical details about mechanics and calculus that would have been bread-and-butter material 100 years agp.
Yes, that makes perfect sense. And it seems like quite a natural spread of information when viewed like that. When you think about it, that pattern of development tends to be the way with a lot of topics. They are founded, then used by the cutting-edge scientists and mathematicians, and then everyone starts learning from one another and putting their own spin on things.
I'm curious about your last sentence, because it sounds intriguing but I'm not quite sure I follow. What do you mean about linear algebra replacing some of the technical details about mechanics and calculus? And are you saying their details aren't bread and butter now in comparison to 100 years ago? Like are there things about mechanics and calculus that are now lost (and not covered in syllabuses) or is it a matter of linear algebra improving said aspects of mechanics and calculus?
@@ciaranmcevoy9875 It was common in high school maths 100 years ago for example to study moments of inertia fo ellipsoids or in depth studies of conic section. These days advanced students in 16-18 education are more likely to encounter matrices, eigenvalues etc. And then at university a lot of maths and physics exams focused on very involved and complicated problems involving classical mechanics and traditional algebraic manipultion - look at the typical questions here: archive.org/details/mathematicalprob00wolsrich/page/n11/mode/2up in 19th century undergad Cambridge Maths tripos exams.
Ah yes, I'm with you now. That is such a good insight and a valid observation. Why do you think the shift has been towards matrices and eigen values etc? My gut feeling would be computational power making the requirement of thorough knowledge of the mathematics of certain aspects such as, like you say for example, conic sections, partly redundant.
By the way, that mathematical Tripos examination booklet looks impressively taxing, makes me want to have a go at a few questions haha.
To me, matrices were boring and unnecessary until I found out that a matrix is just anothe way to present an algebraic straight line. ex 2x +4y = 5 can be presented in a 2 by 2 matrix. And if you have three variables its a 3 by three matrix etc. Human imagination is limited to understand 3 dimensional space, but matrices can deal wit unlimited numbers og dimensions. This mat is widely used in artificial intelligence where each connection between processors has to be calculated. Imagine a neural network with 2048 input processors in 98 rows, with each processor connect to each of the processors in the layer above. and Ai does this in split seconds. I do find this kind of interesting.
He assumed that we knew what you said about representing a straight line with a 2 by 2 matrix. I Didn't. Thank you for your input. I need , now, to find a source to break that down even more for me
This is an excellent explanation of why matrices even exist. We home school, and we just started learning matrices in algebra. My son was very frustrated and asked, "Why do these even exist?" Thank you for answering his question.
I'm so glad to hear that! That makes me very happy to hear.
Amazing vid as always.
After watching 3b1b's *Essence of linear algebra* what I got is
*A Matrix is representation of a linear transformation between two sets of dimensions*
For example: from {carrot 🥕, tea ☕, rose 🌹} to {water 🌊, money 💰}
😅
very good video sir..we really need to know why we learn this stuffs
your videos are amazing ... !!!
Cheers Samir! Much appreciated pal.
thanks, this helps to make me interested at actually learning
I listened to the audiobook on Calculus 'Infinite Powers', which really made Calculus make sense to me. Came here looking for how Matrices transformed and why they were used in history and their evolution through time
I hope the video gave you some of the insight you were looking for :)
Some, thanks. Want to understand the roots more widely
@@practicecoach777 did you find any other resource which goes more into the history of it? If so, plz share. I too am looking to undersand it.
you make boring topics interesting and easy to understand ...
That's great to hear Samir. I'm glad you think that!
Very beautiful vedio and simple language of explanation 🌹🙏🌹
This channel is very underrated ❤
That's a lovely compliment. Thanks Rakesh.
This was cool. 👍😎
Glad you enjoyed it Dexter. More introductory maths history videos are definitely in the pipeline 🍻👍
I really loved your video. Can you work out the corn field problem? You are a good story teller as well !!!
Thank you for your kind words. I'm glad you enjoyed the video. The corn problem can be solved using Gaussian elimination. I've got a video on how to do that here: ua-cam.com/video/6SSld9w792I/v-deo.html. Feel free to have a go and let me know if you need any help, I'd be happy to do an Instagram post with the answer.
Thankyou
You didn't say whay they exist. you just mentioned the history
Hey Abdul, sorry you didn't feel this video answered that question. Though I may not have said it explicitly in a sentence, I believed it was implied from discussing the history. For example, they exist because humans invented them to use with simultaneous equations. After that, further matrices related discoveries were made. But ultimately they began as a way to solve simultaneous equations easier.
Dude if you would level up with a catchy animation style these topics would kill
It's MATH.
wr
Same
A lot of words. Not much information.
Few words. A lot of bs.