1. The Geometry of Linear Equations

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  • Опубликовано: 22 ноя 2024

Комментарии • 807

  • @mitocw
    @mitocw  5 лет назад +960

    Audio channels fixed!

    • @cpcheats2003
      @cpcheats2003 5 лет назад

      Awesome! :D

    • @BentHestad
      @BentHestad 5 лет назад +21

      God Bless You, MiT and Gilbert Strang! You deserve a lot of praise for this series, now in even better quality.

    • @santanumisra4190
      @santanumisra4190 5 лет назад +6

      Thank you MIT OpencourseWare

    • @rj-nj3uk
      @rj-nj3uk 5 лет назад +5

      Mit please provide a series on propositional logic and predicate calculus.

    • @giorgostseligas37
      @giorgostseligas37 5 лет назад +2

      Many thanks to MIT and Professor Strang! We love your work

  • @scottbrandon6244
    @scottbrandon6244 Год назад +1187

    This was filmed in 2005 when Gil was 70. He just retired from MIT this month (May 2023) at age 88 after a 62 year career as a professor. What a great career.

    • @mgh7818
      @mgh7818 Год назад +67

      Wow, he looks so much younger than 70 in this lecture

    • @Peter_1986
      @Peter_1986 Год назад +26

      ​@@mgh7818
      I would have guessed maybe 55-60.

    • @henryfordsonofindia8399
      @henryfordsonofindia8399 Год назад +12

      Was he 70? And retired at 88 this year 😲😲😲

    • @Peter_1986
      @Peter_1986 Год назад +14

      @@henryfordsonofindia8399
      Yeah, he seems to be in very good shape for his age;
      he can walk around in front of the board, and he can juggle around matrix algebra with ease.

    • @lowlightevangelist9431
      @lowlightevangelist9431 Год назад +11

      Fastest moving, smartest 70 year old, prolly ever.

  • @sanchayanmaity5731
    @sanchayanmaity5731 2 года назад +280

    In two years of junior college and 4 years of engineering, not once did anyone gave the column picture explanation. Mind blown. Thank you, Dr. Strang.

  • @BC-hg6dz
    @BC-hg6dz 5 лет назад +782

    Thank you Dr. Strang. I graduated from high school functionally illiterate in math. In my journey to teach myself math you have become a great mentor.

    • @artherladett442
      @artherladett442 5 лет назад +25

      I second this! I was exactly the same!

    • @georgecarlin2656
      @georgecarlin2656 5 лет назад +21

      Me too! Here on Mars good math professors are a scarce resource too!

    • @popeagapitusi8
      @popeagapitusi8 4 года назад

      Good luck!

    • @David-km2ie
      @David-km2ie 4 года назад +4

      Good luck in your amazing journey

    • @maheshnahak9510
      @maheshnahak9510 4 года назад

      @@georgecarlin2656 uhm...MARS????

  • @gerardomoscatelli9035
    @gerardomoscatelli9035 3 года назад +332

    I wish I had teachers like Prof Gilbert Strang when I studied linear algebra. What a difference makes to have someone dedicated to explaining the geometry of what is going on.

    • @nickyork8901
      @nickyork8901 3 года назад +12

      33 years ago I was told to read his book on linear algebra and its applications, my first experience of learning this stuff...did not always work for me, but I persevered with his approach and got there in the end. It's amazing now to see what he actually looks like.

    • @NazriB
      @NazriB 2 года назад +2

      Lies again? Gay Of LA

    • @agz163
      @agz163 5 месяцев назад

      I took this class from him in the 1980s. He was a great instructor.

  • @PhucLe-qs7nx
    @PhucLe-qs7nx 3 года назад +437

    00:00 Course overview
    01:00 Lecture overview
    04:25 Row picture 2D
    08:35 Column picture 2D
    15:38 Row Picture 3D
    22:00 Column Picture 3D
    27:55 Can I solve Ax=b for all b?
    32:25 "Visualise" 9-dimension
    35:33 How to multiply a matrix and a vector?

    • @arisoda
      @arisoda 2 года назад +7

      ​ @MIT OpenCourseWare please copy this info to the video description so it becomes visible in the video timeline

    • @MrJ691
      @MrJ691 11 месяцев назад

      Someone do this for every lecture video

  • @Christopher-mi6qe
    @Christopher-mi6qe 3 года назад +58

    Took 18.06 in 1992 and he taught it. Great stuff, and an awesome professor.

  • @adarshkumar7238
    @adarshkumar7238 4 года назад +264

    Professor strang is master of teaching
    He is an artist.
    His way of teaching is a masterpiece.
    Thank you Sir.
    Respect, from India

    • @maan92cu
      @maan92cu 4 года назад +17

      I'm learning from Saudi Arabia. And I couldn't agree more with what you wrote! God bless him!

    • @SolidSiren
      @SolidSiren 3 года назад +5

      Hmm...I wouldnt go that far. Imho, he is a good teacher from what I've seen here. He clearly cares about teaching, and he engages his students the way a good teacher should. He starts from first principles and assumes next to nothing about his students. But I wouldn't call it artistry or a masterpiece of teaching haha.

    • @MLFranklin
      @MLFranklin 3 года назад +4

      Despite his humble comments, he actually is a Rembrandt.

    • @adarshkumar7238
      @adarshkumar7238 3 года назад

      @@MLFranklin so true

    • @HOWYOUDOIN884
      @HOWYOUDOIN884 3 года назад +6

      Yes... it's interesting how you can't really just rely on a book, and why it helps to watch a person actually doing it. And the style totally is important.

  • @MelodyMcQwerty
    @MelodyMcQwerty 3 года назад +42

    We're using Professor Strang's book in my linear algebra class and I really cannot understand my professor's teaching style. My friend pointed me to these lectures instead and I already feel like I actually understand a lot more from this one lecture than I have the past two weeks in my class. Thanks Professor Strang!

  • @fernandozolubaspreto6976
    @fernandozolubaspreto6976 Год назад +24

    Hi professor and online collegueas. I'm a control engineering student, so Linear Algebra is the essential of my field of study. Despite I've taken a linear algebra course before and even sophisticated discussions in control systems, I never truly understood until now why it is better to think using columns instead of using rows. But now it's totally clear in my mind, so thank you very much, professor Gilbert. I'm anxious for the next classes.

  • @graphchick
    @graphchick Год назад +8

    as a 1st year grad student a very long time ago, i took a course in linear algebra using Gil Strang's book. learning about the relationship between the four fundamental spaces of a matrix felt revelatory at the time, and i still have that book. he's such a wonderful expositor.

  • @douglasstrother6584
    @douglasstrother6584 5 лет назад +59

    It's so important to develop a geometric view of linear algebra.

  • @jaydean5243
    @jaydean5243 9 месяцев назад

    Prof Strang really LOVES teaching, his soul is part of it-they say a genius make poor teachers- he is the one exception- Thank you for your efforts to bring people into your world

  • @marco.nascimento
    @marco.nascimento 4 года назад +51

    An amazing first lecture, glad to see the audio is fixed, thanks for taking care of this course. It's beautiful to perceive people from all over the world gathering here to gain knowledge, Professor Strang is a great teacher

  • @FHB71
    @FHB71 3 года назад +26

    That makes me remember the first semester linear algebra lecture. He certainly takes his time to explain, what the interpretation is and that is wonderful. We were not so lucky unfortunately.

  • @shutupimlearning
    @shutupimlearning 2 года назад +100

    its insane that this video is 15+ years old and still so valuable to someone beginning to learn linear algebra like myself

    • @diegoferrari3341
      @diegoferrari3341 Год назад

      WTF? How old are you? 10? What 15 miserables years are to the Greatness of Mathematics!??? Math rules the Universe!

    • @AbdurrTheK
      @AbdurrTheK Год назад +1

      Same here!!

    • @Dontpushyour_luck
      @Dontpushyour_luck Год назад +23

      Because mathematics doesn't change

    • @davyroger3773
      @davyroger3773 Год назад +3

      @@Dontpushyour_luck Until another Leibniz comes along

    • @tchaivorakfauresohnsieg9532
      @tchaivorakfauresohnsieg9532 Год назад

      Have you finished it, was calculus prerequisite?

  • @BobbyRunout_EverydayWorld
    @BobbyRunout_EverydayWorld 4 года назад +58

    Kept 1st lecture intro to one minute. Bless this man.

    • @matematik-ks3860
      @matematik-ks3860 4 года назад

      Please spread this school on your wall and your friends because students need to see it.
      So will you.
      There are more than 4 000 tasks and theorems for primary and secondary school students.
      Thank you for your contribution.
      Respect! ........................................... .Të lutem shpërndaje këtë shkollë në murin tuaj dhe miqve tuaj, sepse nxënësit kanë nevojë ta shohin.
      Kështu do të kontribosh edhe ti.
      Janë më tepër se 4 000 detyra e teorema për nxënës të shkollave të nivelit fillor dhe të mesëm.
      Faleminderit për kontributin tuaj.
      Respekt!
      ruclips.net/channel/UCELXh5_dCYX6umKP3qlOL9g

  • @sannyii1098
    @sannyii1098 2 года назад

    SO fantastic!!!THE Right way to open Linear Algebra!!! 我是来自中国的学生,当我认真学习线性代数的第一堂课后,我被深深的shocked到了!让我重新理解了维度! N-D space is a combination of N-1-D sapce and non-N-1-D vector!

  • @achievemindsetmastery
    @achievemindsetmastery 4 года назад +40

    Preparing for IIT/IISC M.S interviews. IIT Madras, Electrical Engineering department had recommended this lecture

  • @omeryacine8281
    @omeryacine8281 4 года назад +28

    about to cry of how beautiful this is

  • @mathyscrete9469
    @mathyscrete9469 5 лет назад +428

    For everyone begining this lectures that have no notions of linear algebra, I reccomend you to watch 3Blue1Brown series before because he put a lot of image on the word. Sorry for the mistakes, I am not an english speaker.

    • @osxs333__7
      @osxs333__7 5 лет назад +19

      That series was amazing

    • @HenryTechBoy
      @HenryTechBoy 5 лет назад +22

      Currently watching that series myself and would recommend it as a phenomenal starting point for Linear Algebra @3BLUE1BROWN

    • @osxs333__7
      @osxs333__7 4 года назад +2

      @Chris Metcalf i got my eyes on landing a job in data science for myself, just brushing up the mathematics behind machine learning but definitely not planning on doing deep theoretical tinkering and what not

    • @nerdpotato9368
      @nerdpotato9368 4 года назад +11

      what should i watch? the essence of linear algebra?

    • @mathyscrete9469
      @mathyscrete9469 4 года назад +8

      @@nerdpotato9368 yes

  • @MarceloSantos-hz1bg
    @MarceloSantos-hz1bg 3 года назад +9

    Gracias Dr .Strang ,yo estudie algebra lineal con su libro ,pero verlo a Ud ,explicando en ingles , me llena de emoción , desearóa estar en su clase ,es un genio ,en persona es mas de lo que pueda decir su libro ,Mi admiración y respeto , Que calidad magistral para explicar algo tan ABstracto ,lo hace ver facil y sencillo,tanto que hasta mi hija de 12 años que esta en primaria lo entiende ,es un superhiperExplicador

  • @solfeinberg437
    @solfeinberg437 5 лет назад +16

    This makes me want to applaud. I watched his summary lecture that reiewed this course and I damn near clapped in my home. I should buy his book - I bought another one that's working fine, but didn't emphasize the row space column space null space left null space fundamental theorem of linear algebra picture that this course develops.

  • @SatireDaily
    @SatireDaily 5 лет назад +1233

    humans will start learning machine learning here.

    • @bouthaina7846
      @bouthaina7846 5 лет назад +84

      Yes, I'm here because of machine learning

    • @rezaadventures
      @rezaadventures 5 лет назад +22

      @@bouthaina7846 hi
      can you tell me what is the application of Linear Algebra in ML ?
      I really confiused whit vector space and Scalar field and what we exactly model and do in linear algebra

    • @bouthaina7846
      @bouthaina7846 5 лет назад +21

      @@rezaadventures actually I'm so new and just started studying machine learning but for what I've seen in neural networks, PCA and a lot more things everything is about matrices and linear algebra so I've decided to firstly understand linear algebra then everything else will be quite easy ...

    • @moonriver7632
      @moonriver7632 5 лет назад +7

      @@bouthaina7846 Do u study computer science before or directly do machine learning ?

    • @bouthaina7846
      @bouthaina7846 5 лет назад +2

      @@moonriver7632 yes I studied cs first

  • @paulmerritt418
    @paulmerritt418 3 года назад +11

    I can see why Dr. Strang is a professor at MIT. The best of the best.

  • @testus86
    @testus86 4 года назад +3

    I had 3 semesters math in informatics study. This guy is way better than my prof years ago. He explains it way better

  • @elamvaluthis7268
    @elamvaluthis7268 4 года назад +1

    Superb clarity.world renowned professor of Mathematics.see how he acts on the stage one should inspire.I grace your heels.

  • @kirkyrussell
    @kirkyrussell 3 года назад +28

    I love the quirky teaching style of Prof. Strang, especially how he feigns to encounter something surprising, whereas in fact it is well-rehearsed.

  • @MLFranklin
    @MLFranklin 3 года назад +8

    I had linear algebra over 40 years ago, but this was the first time I'd seen it presented this way. I've done fine in my engineering career, but this kind of thinking would have definitely made a few things easier.

  • @faizanmohsin3685
    @faizanmohsin3685 Год назад +1

    Linear algebra had been mystery for me until I saw these types of lecture online. Thanks

  • @hidetsuguhiraki3307
    @hidetsuguhiraki3307 3 года назад +1

    When we get linear equations, Ax=b, where A is an n x n matrix, and x and b are column vectors with n components, we can see b as the linear combination of column vectors of A and components of x is equals to b. That is,
    column 1 of A * 1st component of x
    + column 2 of A * 2nd component of x ...
    + column n of A * nth component of x.
    This view is new for me. Thank you, Prof. Strang.

  • @nicholasmohr1619
    @nicholasmohr1619 Год назад +4

    Today was Gil’s very last lecture and retirement day. Happy Retirement Dr. Strang!!!

  • @hassannazeer5969
    @hassannazeer5969 2 года назад

    In the first lecture, from 14:10 to 15:26 the dude threw on the gem. If you notice this is the idea of vector spaces something which really you don't understand when you start linear algebra. Moreover, he pushed the argument at 22:00 with all the beauty to show that a column picture is a preferred way of looking when it goes into a higher dimension, the point on which he comes back in vector spaces. Finally, at 28:00 he concludes an important thesis for vector spaces.

  • @frankgao1265
    @frankgao1265 4 года назад +4

    This is best Linear Algebra Course one can find on the internet

  • @animalsilvestre
    @animalsilvestre Год назад +2

    Soy arquitecto, antes de ingresar a la facultad ingresé también a matemática pura, lamentablemente dejé las matematica por la arquitecturas, ahora devoro libros de matemáticas, espero algun dia retomar mi camino, mientras tanto me divierto con sus clases....y la pasión aumenta.
    Saludos!

  • @BACPEP
    @BACPEP 2 года назад +2

    One of the best teachers! As a viewer of this course you feel the passion and love for math. He feels the math and can transfer his knowledge to other people. Well explained! Top!

  • @secheledelaruse1937
    @secheledelaruse1937 Год назад +4

    attend to the strang paradox; a vector field of unfinished sentences that form the basis vectors for a stunning range of interesting algebraic problems

  • @aadarshmishra2504
    @aadarshmishra2504 4 года назад +577

    The cameraman here is now a Senior ML Engineer at Google, California.

    • @aadarshmishra2504
      @aadarshmishra2504 4 года назад +47

      @Bob Smith It's a sarcasm to the fact that how good these lectures actually are. 😅

    • @prashantdhameja5778
      @prashantdhameja5778 4 года назад +8

      @Bob Smith That kinda dumb is acceptable in the nerd academy so no r/wooosh for you.

    • @user-yk6cz3dh9i
      @user-yk6cz3dh9i 4 года назад +2

      @@aadarshmishra2504 very useful

    • @jainpranayr
      @jainpranayr 4 года назад +1

      r/woosh

    • @sigmaswan2969
      @sigmaswan2969 4 года назад +2

      😂

  • @wxie7689
    @wxie7689 2 года назад +4

    Even though I've learned Linalg from my undergraduate course, it was ages ago. Thanks to Prof Strang, the explanation of the geometry meaning of the matrix is much clearer than what I've ever been given.

  • @coemgeincraobhach236
    @coemgeincraobhach236 4 года назад +29

    This might help others trying to learn this material.
    I found it easiest to watch a few lectures, but without being overly concern about learning exactly whats going on. This gives you a basis to work from.
    Then get the text book and work though it slowly. Write down the examples in the book as you encounter them and get used to forming a mental picture for whats going on.
    The column picture is key.
    The row picture is probably what your school math teacher taught you. This just confused me a lot. I don't like dot products, but the "combinations of columns" is very intuitive once you can visualize why it works.
    The reason I found this easier is that the concepts introduced in the videos are a bit loose, its just an overview. The real learning comes from the text book.

  • @davidli5382
    @davidli5382 5 месяцев назад

    I don't think anyone could have explained it as good as this guy, props to him and everyone involved to make this happen!

  • @feruzaerkinovna6052
    @feruzaerkinovna6052 5 лет назад +298

    I always dreamed (and still continue) about studying at MIT, but I am not a genius and not a daughter of some deputy, so instead of university lectures I watch this course and imagine myself studying there))

    • @starzandearth
      @starzandearth 5 лет назад +28

      hopefully you reach there :)

    • @lucianoinso
      @lucianoinso 4 года назад +71

      There's not that much difference on content on the subjects between good universities and the ones at the ivy league, just study for the love of it.

    • @lizzy1138
      @lizzy1138 4 года назад +19

      Luciano Rodriguez this is true. I attend an Ivy League university and paradoxically, the intro level math classes are awful, I study from MIT materials

    • @TigerAlert
      @TigerAlert 4 года назад +4

      I mean you also have to think about the school fees and see if it's worth it. I don't think it's as black and white as you may think, it's probably more grey.

    • @akbarrahmatullah6701
      @akbarrahmatullah6701 4 года назад +2

      That's passion. Great thought.

  • @LordMgls
    @LordMgls Год назад +1

    10 years ago I skipped Lin Algebra class and learned by watching this fantastic series of lectures. Moved to have learned that Prof Strang just retired. A big thank you to him for delivering such well thought through and well paced lectures.

  • @Unknowledgeable1
    @Unknowledgeable1 2 года назад +1

    0:54 the fundamental problem of linear algebra
    - a system of linear equations needs to be solved
    1:13
    1:25
    1:49 "picture a column at a time"
    2:02
    2:12
    2:59
    3:10
    3:34
    3:40 A is the matrix of coefficients
    5:57
    6:23
    The line of solutions to this equation
    8:34
    14:13
    23:44
    26:00 big picture
    29:30 multiplying a matrix by a vector. AX

  • @douzijin6541
    @douzijin6541 5 лет назад +9

    For a person who is not really good at math, I hope this will really help me to develop a big picture of what linear algebra is. Thanks Prof. Strang.

  • @TheWonderworld10
    @TheWonderworld10 2 года назад

    You know a man's the GOAT if lectures from almost 2 decades ago with chalk and a blackboard are better than 90% of the content online. Thank You, Professor Strang and MIT for bringing such amazing content to the world...

  • @inalambricoteseo3082
    @inalambricoteseo3082 5 лет назад +8

    thank you Mr Strang for your lecture!!! i don't understand yet the fact that with 2 millions subscribers, only 4000 folow your lecture!! Your chain is one of the best i found regarding basical science, congratulations!!!

  • @Victual88
    @Victual88 5 месяцев назад

    Thanks for this; the impact of these videos on Linear Algebra education can't be overstated!

  • @brothberg
    @brothberg 2 года назад

    Why is Prof. Strang so successful at teaching? It's not just that his explanations are clear and reasonable. His personal style has a lot to do with it. He comes across as unpretentious and as someone who is doing this journey with you.

  • @randomdude354
    @randomdude354 4 года назад +9

    There are so many moments when I wanted to give this video an extra LIKE! He's such a good teacher!

  • @muttleycrew
    @muttleycrew 2 года назад

    My lecturer in Linear Algebra was pretty good at doing mathematics but he was not so good at explaining it. I have really enjoyed these lectures and came back to the start just to encourage others to watch and enjoy.

  • @ahmedatiatolba
    @ahmedatiatolba 3 года назад +1

    This man is the best LA professor ever and these lectures are perfectly made. I really appreciate Prof. Strang and all the team involved.

  • @bitstsunami9520
    @bitstsunami9520 4 года назад

    guys if you are here because of machine learning then trust me this course is the most most useful one to do before even starting machine learning i can ensue you it worth it 100% i myself have completed this series and it just gave me leg up in ML trust me after this course you will be able to understand ml concept that some of highly paid ML people can't! it will be such a leg up in you ml career i swear i wish i can erase it from my memory and do all it all over again
    p.s please do it right tho understand every concept go through book and do exercise if needed give it good 3 months atleast

  • @piotrek0207
    @piotrek0207 4 года назад +1

    I'm really happy that great lectures are available for free. Young people should appreciate it that they have internet and they can learn from materials from other universities especially from other countries from another part of the globe.

  • @mrnobody1321
    @mrnobody1321 3 года назад +3

    Can't remember last time i was so pleased learning maths, apart from a few 3b1b vids.
    Thanks Sr.

  • @tomshabalin9775
    @tomshabalin9775 3 года назад +13

    I'm a student in Ariel University at Israel. I'm studying computer science and math, and I just want to say that you are a terrific teacher!
    I will recommend your lectures to my friends for sure!
    Thank you a lot.

    • @bazmira3283
      @bazmira3283 11 месяцев назад +2

      Free Palestine

    • @ayushsen6393
      @ayushsen6393 28 дней назад

      does this mean that in aany country most people do not study from college clases

  • @vensoltface4506
    @vensoltface4506 5 лет назад +8

    I'm studying in McGill and this man is saving lives. Ofc, cramming before the finals :D God bless this man. Watched his videos on 1.25x speed

    • @emilefortier1688
      @emilefortier1688 4 года назад

      Nice to see a fellow McGillian! I graduated in 2016.

  • @douglasstrother6584
    @douglasstrother6584 5 лет назад +21

    I like the column perspective.

  • @Ali_Aquiles
    @Ali_Aquiles Год назад

    I don't want to write down a big definition, you can see what it is."
    how much we need teachers like this.

  • @biswabismitabag9017
    @biswabismitabag9017 5 лет назад +15

    Thank you MIT OpenCourseWare..Prof. Strang is God, Not only MIT students the whole World deserves a great teacher like him.
    A student from India

    • @aarayan111
      @aarayan111 4 года назад

      this course is good for under graduate student

  • @ahmedabbas3998
    @ahmedabbas3998 3 года назад

    The clearest explanation with clearest English. That accent is very clear and manly.

  • @achieverakash5192
    @achieverakash5192 3 месяца назад +2

    In my whole life never did this matrix multiplication make me sense like why are we doing multiplication and addition to numbers in a box in a specific manner, which is very non-intuitive, But the column picture idea that you gave makes me think it is matrix is an awesome tool to the equations

  • @someoneyouIoved
    @someoneyouIoved Год назад

    thats the greatest explanation of geometry of linear equations i have ever seen, thank you for everything sir, greetings from istanbul technical university

  • @dhairyashah1746
    @dhairyashah1746 4 года назад +6

    Dr Strang is a Legend, Thank u Sir and MIT for this awesome
    course

  • @aaronbell5994
    @aaronbell5994 5 лет назад +43

    Wait, this was published 4 days before I decided I needed this? Thank you!

    • @ath216
      @ath216 5 лет назад +3

      i guess they have re-uploaded the video again after fixing the audio channels. check their pinned comment before 1 month ! enjoy :)

  • @lovemoremadzongonye2624
    @lovemoremadzongonye2624 3 года назад +1

    Linear Algebra runs in his blood (Prof. Gilbert Strang). I now understand Linea Algebra thanks to his amazing lectures and his too much insight into this subject!!! He opens mind and unlocks concepts which are not naturally easy to grasp.

  • @apdy
    @apdy Год назад

    24:44 thanks to prof. strang that he didn't get away by just taking an easy example and explained other cases where it didn't work.
    .
    .
    .
    32:20 the way professor strang visualise the 9 dimensions is so impressive

  • @acho8387
    @acho8387 2 года назад +2

    So many questions answered in 40 minutes. Thank you so much, Professor Strang.

  • @BuddyNovinski
    @BuddyNovinski 2 года назад +1

    So, that's the reason for the row versus the column combinations! I could've used this concept in late 1976.

  • @davidwilkie9551
    @davidwilkie9551 Год назад

    "It's the right place to start".. now, ..continuous observation of logarithmic 0-1-2-ness Polar-Cartesian i-reflection z axis containment in/of the x-y plane vector-value, convergent con-sequence, positioning. This is the "long hand" breakdown of pure-math Actuality, point-line-circle log-antilog conic-cyclonic coherence-cohesion Timing-Spacing.

  • @jacobsabanin8128
    @jacobsabanin8128 5 лет назад +22

    Collect Mr Strang's lectures like a puzzle now (Because he's really good)

  • @deepakkumarkhatri
    @deepakkumarkhatri 2 года назад

    Really got the points!
    First time in my life I have completed a lecture on math and also learned multiple new things!
    All concepts got cleared.
    Thank you Gilbert Strang for introducing me to LA.
    Respect++;

  • @HWPcville
    @HWPcville 3 года назад +1

    I enjoyed this lecture. Professor Strang seems like a congenial person truly interested in imparting his knowledge. Some professors seem to look down on their students and have the attitude that if you don't get it, tough.

  • @eduardovieira7001
    @eduardovieira7001 Год назад +1

    That’s why people goes to MIT. What a class!

  • @vsshappy
    @vsshappy 3 года назад

    Linear Algebra has been my good old friend for several decades, but now I see a fresh look at my friend that looks much younger, all this thanks to the amazing profession Prof. Dr. Gilbert Strang. The essence of the timeless reverence Guru Brahma proved again. I shall be going through the entire series, even though, I wish I had this opportunity a decade and half ago. 🙏

  • @samiulislam6527
    @samiulislam6527 4 года назад +9

    The Business Analytics admission director for McCombs school of business told me to watch these videos for a understanding of linear algebra.

  • @gulustanmustafaqizi6816
    @gulustanmustafaqizi6816 4 года назад +1

    Thank you Dr. Gilbert Strang. I am a senior lecturer at Azerbaijan State Agrarian University. I teach the subject Linear Algebrain in English . You explain very clearly.

  • @fireblizzard2287
    @fireblizzard2287 3 года назад +3

    I came here just for fun, but end up knowing something new. A new and easy method to multiply matrix. Thank you so much 🥰

  • @nomiwang10
    @nomiwang10 6 месяцев назад

    I passed my linear algebra with a 100%but I literally didn’t know shit why those are happening. Thank you Dr Strang for letting us know what is linear algebra truly about.

  • @muzou520
    @muzou520 3 года назад +5

    This is an amazing lecture for Linear Algebra. Thank you Prof. Strang!

  • @石武-b5u
    @石武-b5u 7 дней назад

    Even his voice sounds like a professor. Thanks for the upload!!🎉

  • @linustiberiusgartner4177
    @linustiberiusgartner4177 3 года назад +1

    At 20:50 This is why studying at MIT is worth the tuition. Great teacher!

  • @SuperReddevil23
    @SuperReddevil23 4 года назад +4

    Comman man's Justice League:- Batman, Superman, Wonderwoman, Aquaman
    My Justice League:- Gilbert Strang, Walter Lewin, Ben Polak, Patrick JMT, Ben Lambert

  • @Ernesto1317
    @Ernesto1317 4 года назад +25

    I can see in the class of this excellent professor and mathematician what the real problem in mathematical education is: our obsession to cover the topics always skips the necessity of the students to form the proper intuition of a topic. Intuition takes time, but above all takes proper activities to develop it. His talk is basically about the generation of spaces through linear combinations, but honestly could anyone sitting down there and listening reproduce those ideas without the help of proper representations, say, software, or at least good pictures? In mathematics, physics etc, intuition is the most important, but scholastic education has always tortured them with logic. That is totally unfair and a waste of talented students.

    • @davidjohnson497
      @davidjohnson497 3 года назад

      Why u say it is devoid of intuition when he is showing exact steps of logic? Sure, u may miss understanding the steps of logic, but nothing he is saying depends on intuition! Follow the formula correctly, get the right answer! Make a mistake in calculating, get the wrong answer!

    • @NinjaRunningWild
      @NinjaRunningWild 2 года назад +1

      @@davidjohnson497 🤦‍♂️

    • @brahimoukhouya5888
      @brahimoukhouya5888 2 года назад

      U can pause and think for yourself.

  • @solarestone
    @solarestone 2 года назад

    Explaining the 3 planes converge on a point doesn't require a visual aid: two intersecting planes meet in a line such that they are perpendicular to each other along the z axis, the line on that z axis intersecting a third plane on that z axis is perceived as a dot in that z plane. The dot is the product derived by the 3 intersecting planes.

  • @ShivamAnandSpeaker
    @ShivamAnandSpeaker Год назад +4

    My term 2 (semester 2) is about to start. There we have maths 2 and to prepare myself for that I am here.My Senior suggested me this.
    I am in foundation level (1st year) of IIT MADRAS (India) BS in Data Science and Applications.
    Seems good one!
    Yet to explore more!
    By the way Thanks to Respected Prof Gilbert and MIT.

    • @akshatgupta8199
      @akshatgupta8199 Год назад +1

      Hii! I'm the same case as you, preparing for maths 2

  • @metacortex4140
    @metacortex4140 4 года назад +47

    Well boys, future starts here.

  • @ASDCarGuy
    @ASDCarGuy 4 месяца назад

    Studying for fun. Thanks for a beautiful lecture. Way to connect the dots, literally

  • @aligator7181
    @aligator7181 3 года назад

    Hot off the presses : We can pair every positive floating point number
    using up only about 20% of the integers
    Algorithm #1 : Convert a float with a zero whole part into an integer
    1. Reverse the character sequence representing this float
    2. Remove the decimal point to obtain the desired integer
    Example : Convert the float 0.002743 into its integer equivalent
    1. Reverse the float string to obtain 347200.0
    2. Remove the decimal point to obtain the integer 3472000
    3. Note : All corresponding integers will be terminated by the character “0”
    Algorithm #2 : Convert a float with a non-zero whole part into an integer
    1. Count the number of whole digits or NWD (those preceding the decimal point )
    2. Append a number of “0” digits equal to NWD to the float.
    3. Append a digit “1” to the resulting float
    4. Remove the decimal point to obtain the desired integer
    Example : Convert the float 1230.0098 into its integer equivalent
    1. Count the number of whole digits : NWD = 4
    2. Append NWD = 4 “0” digits to obtain 1230.00980000
    3. Append a digit “1” to obtain 1230.009800001
    4. Remove the decimal point : this gives us the final integer of 1230009800001
    Note : We append a digit “1” to distinguish the integers derived from floats with
    non-zero whole parts from integers generated by floats with zero whole parts .
    This can be done for every float [whole.fraction] where whole > 0 !!! AMAZING!!!
    We just came up with a scheme which pairs each positive float with a positive integer.
    Reverse Algorithms : Converting valid syntax integers into floats also exist

  • @wayneyadams
    @wayneyadams Год назад

    I have always preferred solving linear equations with matrices, it is my go-to method. I like it because it is faster, saves me from having to write all the variables at each step, and because it is so neat and compact makes it easier to find errors.
    5:00 It's always easier to rearrange the equations to the point-slope form which makes plotting so much easier. y = 2x, and y = x/2 + 3/2.
    13:00 It would be more helpful to draw the resultant vector, (0,3) first so the target is plainly visible.

  • @anaghpandey8805
    @anaghpandey8805 Год назад +4

    The only disappointment for me is the fact that Prof. Strang can't see my submission to his excellence and gratitude for his contribution, as I feel every time I see him.

  • @mujdatbasaran1070
    @mujdatbasaran1070 Год назад

    In operatins research class, im trying to explain this concept. Some people think that its unrelated. Im happy to see somebody trying to give the same concept to the students at the start of the class😊

  • @joaocabral3541
    @joaocabral3541 4 года назад +2

    I olny had math until 6th form (around 12th grade) and i was invited one day to see a matrix class.
    And let me tell after the first 14 minutes of this video i really felt in love with maths

  • @luisbernier326
    @luisbernier326 Год назад

    God bless him.
    Thanks x 100 times for sharing this video.
    I watch all the videos about Professor Gilbert Strang.

  • @reubenlemba388
    @reubenlemba388 2 года назад

    I like the the way you are analyzing the questions

  • @venkybabu8140
    @venkybabu8140 Год назад

    Any linear equations work for higher powers so they are independent of dimensions. Like 5 x square plus 6 y square equals 20. So dimensions are just reflections. It is true for even vector cross and dot. That's why biological forms and animals forms are cranked. Though vegetations are straight.

  • @melontusk7358
    @melontusk7358 4 года назад

    This is so helpful. I adore professor Gilbert so much. It was a bit surprising to go straight into linear equations at first, but it worked out in the end.

    • @matematik-ks3860
      @matematik-ks3860 4 года назад

      Please spread this school on your wall and your friends because students need to see it.
      So will you.
      There are more than 4 000 tasks and theorems for primary and secondary school students.
      Thank you for your contribution.
      Respect! ........................................... .Të lutem shpërndaje këtë shkollë në murin tuaj dhe miqve tuaj, sepse nxënësit kanë nevojë ta shohin.
      Kështu do të kontribosh edhe ti.
      Janë më tepër se 4 000 detyra e teorema për nxënës të shkollave të nivelit fillor dhe të mesëm.
      Faleminderit për kontributin tuaj.
      Respekt!
      ruclips.net/channel/UCELXh5_dCYX6umKP3qlOL9g

  • @immortalhades1609
    @immortalhades1609 4 года назад +1

    Man this is the definition of LECTURE.....❤️❤️

  • @shivammahajan303
    @shivammahajan303 4 месяца назад

    I'm gonna learn linear programming for economic planning. Thanks for the linear algebra lectures!

  • @camillojimmyfiorito9660
    @camillojimmyfiorito9660 2 года назад

    It's easier thinking a matrix as a linear combination of columns! Tank you, mr Strang.