Independence, Basis, and Dimension

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  • Опубликовано: 2 янв 2025

Комментарии • 295

  • @valeriereid2337
    @valeriereid2337 3 года назад +250

    I am certainly glad to see a professor who teaches from his brain, not reading from power point slides. This is refreshing.

    • @doyochi02
      @doyochi02 2 года назад +4

      lol I'm about to say that

    • @Ztingjammer
      @Ztingjammer Год назад +6

      It most certainly is! It's so captivating as well.

  • @jmr218
    @jmr218 7 лет назад +769

    Wow, the first 2 minutes of this lecture explain the topics better than 1.5 hours listening to my current teachers.

    • @vladkovalenko9222
      @vladkovalenko9222 5 лет назад +2

      True)

    • @RazorM97
      @RazorM97 5 лет назад +1

      I so agree, wow

    • @HK-sw3vi
      @HK-sw3vi 4 года назад +9

      you weren't paying attention in the class, let's be real

    • @calvinmata56
      @calvinmata56 4 года назад

      @@HK-sw3vi No my teacher just has a VERY heavy accent and he wasn't on rate my professor so I went in blind.

    • @AllRounder-jt1pe
      @AllRounder-jt1pe 4 года назад

      In which college u r ??

  • @SilverArro
    @SilverArro 8 лет назад +371

    All math and engineering majors should be required to learn Linear Algebra from Dr. Strang. His lectures are beautiful, crystal clear, and emphasize the big ideas of the subject, and how they connect to one another.

    • @lucasm4299
      @lucasm4299 6 лет назад +2

      Arlo
      I wouldn’t say crystal clear in my opinion.

    • @mikem9270
      @mikem9270 6 лет назад +12

      @@lucasm4299 compared to my professor, clearer than crystal XD ... My professor shouldnt be allowed teach

    • @RutwikGulakala
      @RutwikGulakala 6 лет назад +9

      @@mikem9270 I agree. My professor couldn't explain what Dependent and Independent vectors are properly and every student in the class lost their shit.

    • @duelingo8731
      @duelingo8731 2 месяца назад

      @@lucasm4299 Wdym lmao he was super clear. I watched so many vids never understood it until I learnt it from this guy

  • @divutiful
    @divutiful 4 года назад +24

    It's a treat to the brain. He is explaining like a person does not know anything about the topic but still can go through the lecture. Hats off to the professor here.

  • @cristinabosch
    @cristinabosch 6 лет назад +107

    GILBERT STRANG, YOU ARE A GIFT FROM THE HEAVENS!!!!!!!!!!!!!!!!!! I HAD NOT UNDERSTOOD ANY LINEAR ALGEBRA WITH MY LECTURER AND YOU ARE NOW SAVING MY LIFE!!! YOU ARE B E A U T I F U L , thanks for changing my life 😩😩😩😩

  • @andrescm1022
    @andrescm1022 7 лет назад +118

    Man... Wish my linear Algebra classes were as half as good as this one...
    This is simply beautiful.

  • @water7875
    @water7875 7 лет назад +105

    This dude wrote the text book im referring for linear algebra! His lectures are as amazing as his book!

    • @chandrapandey822
      @chandrapandey822 7 лет назад

      mustard seed
      Yup and most importantly it talks abt. the APPLICATIONS which is more important.

    • @chandrapandey822
      @chandrapandey822 7 лет назад

      mustard seed
      But sadly I have the book in PDF format..

    • @josephgeorge2513
      @josephgeorge2513 6 лет назад

      Can you email me the pdf or direct me to it

    • @monaal.8494
      @monaal.8494 6 лет назад +1

      What is the name of his book please!

    • @emma.muhleman
      @emma.muhleman 4 года назад +1

      I WANT HIS BOOK! Expensive though, you can't get it free, right?

  • @vongxiong5125
    @vongxiong5125 7 лет назад +408

    1,0,0 is a better A3... then.. that loser, that 6,3,5.
    LOL he's halarious.

  • @rickeyaustin7649
    @rickeyaustin7649 7 лет назад +30

    First video in the series Dr. Strang did not start with "Okay!". I love the work he has done and his effort to provide quality teaching to the world! Thank you!

  • @DiyangWu-u4u
    @DiyangWu-u4u 2 месяца назад +2

    Gilbert Strang, the author of Introduction to Linear Algebra, explains this concept better in 13 minutes than all of my other professors can in 3+ hours

  • @johnxiaoyuzhang8961
    @johnxiaoyuzhang8961 2 года назад +7

    I am glad people like me who did not get into MIT can take MIT courses. All the videos I saw from MIT are very clear, easy to follow, and well-structured! amazing

  • @ragsiruh
    @ragsiruh 6 лет назад +11

    A beautiful lecture! For the first time I understand basic terminology of Linear Algebra! Phew! There's a special place in heaven for you. There's a reason why MIT is MIT

  • @jwyliecullick8976
    @jwyliecullick8976 4 года назад +2

    This lecture series shows vast improvement over previous eras; its total lack of fluff, jokes, anecdotes, it's just non-stop content in a nice little 13 minute package. I'm reviewing in the background, it's a great refresher even if oriented towards new students.

  • @farrugiamarc0
    @farrugiamarc0 Год назад

    It is amazing how Professor Gilbert Strang manages to explain such an abstract mathematical topic with so much detail, yet making it easy to understand. He has all the qualities of a good teacher.

  • @LICHKING55Show
    @LICHKING55Show 5 лет назад +3

    Thank the lord for this man. My teacher can't teach in a way that makes sense for his students, but Dr. Strang made it all make sense.

  • @souvikcseiitk
    @souvikcseiitk 2 года назад +1

    First 2 minutes of the video are more than sufficient to kick off any vector space problem you'll ever face in exams. Thanks for preserving quality education, I am really fed up with brainless professors these days trying to print formulas in brain. Thanks MIT and IIT for preserving quality education

  • @alvinaawan884
    @alvinaawan884 4 года назад +3

    You are a life saver, huge respect for the way you teach. Finally I understood all of the concepts after struggling for about one year. Hatsoff. Thankyou so much Sir

  • @zhaomike952
    @zhaomike952 4 года назад +2

    The best professor I've ever seen. There is the MIT!

  • @lightcapmath2777
    @lightcapmath2777 3 года назад

    Am reviewing LA and have not done it in over 20 years. This first lecture of Dr.S, as many have commented, is very clear and simple. Thank you Dr. S DVD:)

  • @vocdex
    @vocdex 6 лет назад +3

    Thanks to Dr Strang, I can now visualize what does all concepts represent. The things are very clear right now.

  • @stalins1383
    @stalins1383 8 лет назад +25

    You are amazing sir... Education is all about transferring your intuition to others... You always great in that.

  • @steve8219
    @steve8219 4 года назад +3

    Oh god, I paid $6000 for a Maths course in uni and barely understand teacher talking about, and it turns out free RUclips video helped me understand every single concept. Imao

  • @funghang3482
    @funghang3482 6 лет назад +12

    professor like Dr strang produces brilliant student , and the student are the reputation of the university . 20 lecture of my professor= 13 min lecture of Dr strang .

  • @이슬스
    @이슬스 2 года назад

    My deepest respect to Professor Strang. Respect to his perennial enthusiasm, and all those years he had devoted to his field.

  • @RC-bm9mf
    @RC-bm9mf 5 лет назад

    Prof Strang, you are now deeply thanked by a man living far far away from the USA. God bless you, God bless MIT, and God bless America!

    • @RC-bm9mf
      @RC-bm9mf 5 лет назад

      Now the idea is crystal clear in my mind. It has taken more than 5 years for me to get this and it happened in just 13 minutes. Thank you. Thank you.

  • @cainmorano4956
    @cainmorano4956 11 месяцев назад +1

    He called one of the vectors a loser. Thumbs up for this video. Also, Strang is great because he keeps simple. KISS is too long and he knew this. It's KS, and the K is only there for clarity.

  • @jkim9931
    @jkim9931 4 года назад +1

    9:55 dimension = # of basis vectors for the subspace

  • @DIVYPAREEK-v3t
    @DIVYPAREEK-v3t Год назад +1

    this is the best lecture so far

  • @ahmedkhalifa9333
    @ahmedkhalifa9333 2 года назад

    One like is certainly not enough for your enthusiasm and dedication Prof. Strang.

  • @omkarkhare9160
    @omkarkhare9160 6 лет назад +2

    such an awesome guy! That's how math should be taught! You can never get bored while hearing Dr Strang's lectures..

  • @arjunag7553
    @arjunag7553 11 месяцев назад

    Been wracking my brain for two days..listened to one line of his explanation and I got all the clarity in the world.

  • @Lena-wn2lg
    @Lena-wn2lg Год назад

    Professor Strang is a genius math teacher!! This is how math should be taught.

  • @samarathrodriguez7662
    @samarathrodriguez7662 7 лет назад +8

    Every time I watch Strang's videos everything makes so much sense and I wonder why I hate Linear Algebra so much.

  • @georgesadler7830
    @georgesadler7830 3 года назад +1

    These topics are important in linear algebra. DR. Strang explains these topics very well in the video.

  • @falconlin419
    @falconlin419 Год назад

    You're the best, professor. I am studying from the 18.06 in spring 2010 and you explain everything very clear. Thank you!

  • @deadbutworking
    @deadbutworking 4 года назад +1

    God what a godsend .. been trying to get these simple concepts for so long and finally one video did it!

  • @IMadeOfClay
    @IMadeOfClay 9 месяцев назад +3

    4:30: Professor Strang was brutal on a3 😂

  • @ComfyDyl
    @ComfyDyl Год назад

    you are a legend, this is so much more clear than any other explanations ive seen

  • @Googk
    @Googk 3 года назад

    Subspace: không gian con
    Basis: cơ sở của vectơ
    Column: cột
    Dimension: số chiều

  • @DrChillg00d
    @DrChillg00d 5 лет назад +1

    5 sections of gibberish laid out in 13 totally crystal clear minuets. good lord this is magic

  • @EsKaioS
    @EsKaioS 6 лет назад

    i finally understood after just 13 minutes of his lecture compared to the 1.5 hours rewatching my uni's lectures and trying to figure out what a basis is. Thankyouthankyouthankyouthankyou

  • @suryanshshukla7384
    @suryanshshukla7384 3 года назад +1

    This is best explaination i have listen for basis, dimension and subspace. It explains everything with connecting one idea to another.

  • @andizvlogs
    @andizvlogs 6 лет назад

    I came from the lecs of linear algebra of 2005 , and i see how him grew up, omg, he is the best!!! i wish i has professors like him.

  • @WestOfEarth
    @WestOfEarth 5 лет назад

    What a pleasure it would've been to study mathematics under Dr. Strang, and physics under Dr. Feynman. Two luminaries who cut through the jargon and teach.

  • @laurencealanano2495
    @laurencealanano2495 4 года назад

    WOW, he really made it more easier for me to understand and his really good! I like how he explain the concepts and meaning of those terms first before teaching about it.

  • @khushaalnandwani3372
    @khushaalnandwani3372 4 года назад

    Subspace explained beautifully at @8:00

  • @srirampallav2765
    @srirampallav2765 4 года назад

    Thank you so much . Have been trying to understand this concept but haven't found a right source which emphasizes on the practicality of the content rather than a textbook definition until this elegant lecture.

  • @royah5404
    @royah5404 8 лет назад +14

    explained very well. wish he is my professor! thank you!

    • @ahsan400
      @ahsan400 7 лет назад +8

      He is your professor. Aren't you studying from him? If yes, then he is :)

  • @xblockitv
    @xblockitv 5 лет назад

    Lemma if f: A -. B is an affine map then the map L,: A-a -. B-f(a) defined by
    4(x) = f(x+a) -f(a)
    is a linear map. The map f is obtained from Lo by the previous construction.

  • @dhrubajyotipaul8204
    @dhrubajyotipaul8204 Год назад

    This was so simply explained that I'm in tears. THANK YOUUUU!!! ♥♥♥

  • @AyushBhattfe
    @AyushBhattfe 7 лет назад +7

    I read the book, then I come to Strang's lectures and I am always all like "oh wtf, yeah it makes sense now"

  • @honkhonk8009
    @honkhonk8009 Год назад

    god i love this guy. hes so chill bro.
    Explained everything perfectly. Damn

  • @benrow5472
    @benrow5472 7 лет назад +1

    you're the man Gilbert Strang.

  • @dabeeramir1407
    @dabeeramir1407 Год назад

    Amazingly explained, I've been trying to figure out this stuff for so long and you explained it beautifully

  • @douglasvargasdasilva7537
    @douglasvargasdasilva7537 6 лет назад

    Hi, I would like to thank this gentleman for the idea of the dimension presented. It will help me better understand the definitions of Linear Algebra books.

  • @ruskodudesko9679
    @ruskodudesko9679 7 лет назад

    beautiful explaination bringing key concepts together, adding visuals and bringing them to life! This is one of the greatest explanations I have heard in my education thus far.

  • @letlhogonolonape849
    @letlhogonolonape849 7 лет назад +3

    Thank you sir, you really helped me. This video is soo understandable. You explain everything soo well. This is full of information and short at the same time

  • @ianbridges6040
    @ianbridges6040 3 года назад

    Thank you MIT OCW and Dr. Strang!

  • @kanikabagree1084
    @kanikabagree1084 4 года назад

    Best teacher i've come across thankyou so much for saving us 😭

  • @karangujarati4589
    @karangujarati4589 5 лет назад +1

    So good to hear and learn from u sir,
    Clear my fundamental about dimensions and basis very well. Yup better than hours of class 🤟🏻

  • @Sky-pg6xy
    @Sky-pg6xy 5 лет назад

    His voice makes learning Linear Algebra fun

  • @Aventinium
    @Aventinium 10 месяцев назад

    Basis is a bunch of vectors and dimension is how many vectors.
    In a single sentence, he sums up what wasn't made clear in so many other lessons and videos and lectures.

  • @d.n.aengineering1485
    @d.n.aengineering1485 6 лет назад

    Excellent explanation with full understanding......and i think i can now clear this topic with a little bit of example solvings....never found such a good explaning teacher than sir. Dr. Strang

  • @damiantoddwell5439
    @damiantoddwell5439 6 лет назад

    Thank you professor.. Now i have finally understood something that has been puzzling me for a week..

  • @nora-xk6gv
    @nora-xk6gv 7 лет назад +1

    you deserve the whole respect Prof I would like to thank you so much .

  • @michaeltheisen
    @michaeltheisen 2 года назад

    10:10 explained Dimensions for me so much better than the textbook.

  • @NothingMaster
    @NothingMaster 5 лет назад +1

    “That loser 6, 3, 5” 😂 Strang is an exceptionally gifted lecturer And an absolute straight-faced blast. LOL

  • @danieladeba206
    @danieladeba206 3 года назад

    Wow!I have never seen such like lecturer....amazing, brilliant for sure!!

  • @Synconntez
    @Synconntez 4 года назад +2

    This guy CAN TEACH!

  • @jas_n1580
    @jas_n1580 4 года назад

    This man is such a treasure! Great lecture

  • @kaiserluvsmariel
    @kaiserluvsmariel 4 года назад

    You're an angel sent from heaven! Thank you so much for these wonderful videos!!!

  • @vrclckd-zz3pv
    @vrclckd-zz3pv 2 года назад

    This video provided me with a very Strang introduction to the concepts. Thank you.

  • @dtalmood
    @dtalmood 5 лет назад +1

    This guy is the real MVP

  • @stevenshi9012
    @stevenshi9012 3 года назад

    thank you! Dr. Strang. You invoke my interest in math as a math student!

  • @jamesgreat5263
    @jamesgreat5263 2 месяца назад

    Damn that's in MIT, this was gold

  • @akashverma1640
    @akashverma1640 6 лет назад

    This video cleared all the ambiguities of mine related to these terms a big thanks to Sir....

  • @makuwaniblessing743
    @makuwaniblessing743 4 года назад

    2020 and you are still good proff

  • @TonyTorzido
    @TonyTorzido 3 года назад

    Bruh what a G. He made it super easy. Thanks, profe

  • @publicplace2034
    @publicplace2034 Год назад +1

    It's Amazing sir,

  • @Michael-ud4wr
    @Michael-ud4wr 8 лет назад +12

    This guy is great

    • @denizerol1
      @denizerol1 4 года назад

      not like that 6 3 5 that guy is a loser

  • @MohamedAhmed-fq6yy
    @MohamedAhmed-fq6yy 3 года назад

    I wanna hug this man

  • @zombie-blood-490gaming5
    @zombie-blood-490gaming5 5 лет назад +3

    god bless you sir, i havent understood this this shit for 3 months till i found this video!

  • @AjayKumar-zq7vm
    @AjayKumar-zq7vm 6 лет назад +1

    Make some more videos like this because there is no good education in my institution
    We thank you for sharing such informative video with us

  • @erickhumalo1913
    @erickhumalo1913 5 лет назад +1

    You're a Legend Madala
    Thank you so much

  • @100yearsofsolitudful
    @100yearsofsolitudful 7 лет назад

    ive never had it explained so well like this, thanks

  • @lolnets5832
    @lolnets5832 5 лет назад

    this is a man of the people....congrats

  • @sunnyvishnoi4310
    @sunnyvishnoi4310 Год назад

    Wow! What a brilliant explanation. Living legend❤

  • @EdorahVtuber
    @EdorahVtuber 5 лет назад +1

    omfg i love this guy and his explanations actually make sense!

  • @centerfield6339
    @centerfield6339 Месяц назад +1

    This was even clearer than the 3blue1brown version. Which is saying something.

  • @stewartmoore5158
    @stewartmoore5158 5 лет назад

    A true math hero.

  • @CocoGras
    @CocoGras 5 лет назад

    Thank you so much for sharing these lectures-- You've helped me so much!! Pure love!!

  • @simonthomas5848
    @simonthomas5848 5 лет назад +1

    I love you sir!!! you are a healer!

  • @distilledleemupaani9232
    @distilledleemupaani9232 5 лет назад

    what did he mean when he said that the plane formed inside 3D vector space is not the same as R^2 at 12:20

    • @elyepes19
      @elyepes19 3 года назад

      Not "ordinary 2d plane" because it's defined by the particular choice of basis vectors. He is impling that the choice of basis vectors for that plane is infinite.
      Also, that there are infinite 2d planes in R3, but for those to be subspaces of R3, they must, by definition, contain the zero vector

  • @pragmatic_p8
    @pragmatic_p8 4 месяца назад

    he explained 15 classes of university's schedule in 15 minutes!!

  • @Humble.fool05
    @Humble.fool05 6 лет назад

    Finally got the idea of basis right. Thanks, Prof Strang!

  • @benzeltser9851
    @benzeltser9851 4 года назад

    SO MUCH BETTER THAN MY TEACHER

  • @munipradeep3314
    @munipradeep3314 6 лет назад

    Super neat with microscopic clarity

  • @logio7663
    @logio7663 7 лет назад +1

    I wish I could learn from him everyday

  • @aprillam227
    @aprillam227 5 лет назад +1

    super cool. such a life saver for my exam!

  • @rot1869
    @rot1869 2 года назад +1

    God bless this guy