Independence, Basis, and Dimension

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  • เผยแพร่เมื่อ 23 ธ.ค. 2024

ความคิดเห็น • 295

  • @valeriereid2337
    @valeriereid2337 3 ปีที่แล้ว +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 ปีที่แล้ว +4

      lol I'm about to say that

    • @Ztingjammer
      @Ztingjammer ปีที่แล้ว +6

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

  • @divutiful
    @divutiful 4 ปีที่แล้ว +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.

  • @jmr218
    @jmr218 7 ปีที่แล้ว +768

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

    • @vladkovalenko9222
      @vladkovalenko9222 5 ปีที่แล้ว +2

      True)

    • @RazorM97
      @RazorM97 5 ปีที่แล้ว +1

      I so agree, wow

    • @HK-sw3vi
      @HK-sw3vi 4 ปีที่แล้ว +9

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

    • @calvinmata56
      @calvinmata56 4 ปีที่แล้ว

      @@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 ปีที่แล้ว

      In which college u r ??

  • @andrescm1022
    @andrescm1022 7 ปีที่แล้ว +118

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

  • @SilverArro
    @SilverArro 8 ปีที่แล้ว +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 ปีที่แล้ว +2

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

    • @mikem9270
      @mikem9270 6 ปีที่แล้ว +12

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

    • @RutwikGulakala
      @RutwikGulakala 6 ปีที่แล้ว +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 หลายเดือนก่อน

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

  • @cristinabosch
    @cristinabosch 6 ปีที่แล้ว +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 😩😩😩😩

  • @rickeyaustin7649
    @rickeyaustin7649 7 ปีที่แล้ว +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!

  • @water7875
    @water7875 7 ปีที่แล้ว +105

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

    • @chandrapandey822
      @chandrapandey822 7 ปีที่แล้ว

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

    • @chandrapandey822
      @chandrapandey822 7 ปีที่แล้ว

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

    • @josephgeorge2513
      @josephgeorge2513 6 ปีที่แล้ว

      Can you email me the pdf or direct me to it

    • @monaal.8494
      @monaal.8494 6 ปีที่แล้ว +1

      What is the name of his book please!

    • @emma.muhleman
      @emma.muhleman 4 ปีที่แล้ว +1

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

  • @DiyangWu-u4u
    @DiyangWu-u4u 2 หลายเดือนก่อน +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

  • @ragsiruh
    @ragsiruh 6 ปีที่แล้ว +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

  • @farrugiamarc0
    @farrugiamarc0 ปีที่แล้ว

    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.

  • @jwyliecullick8976
    @jwyliecullick8976 4 ปีที่แล้ว +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.

  • @steve8219
    @steve8219 4 ปีที่แล้ว +3

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

  • @LICHKING55Show
    @LICHKING55Show 5 ปีที่แล้ว +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.

  • @johnxiaoyuzhang8961
    @johnxiaoyuzhang8961 2 ปีที่แล้ว +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

  • @souvikcseiitk
    @souvikcseiitk ปีที่แล้ว +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

  • @jkim9931
    @jkim9931 3 ปีที่แล้ว +1

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

  • @vongxiong5125
    @vongxiong5125 7 ปีที่แล้ว +408

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

  • @이슬스
    @이슬스 2 ปีที่แล้ว

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

  • @zhaomike952
    @zhaomike952 4 ปีที่แล้ว +2

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

  • @DIVYPAREEK-v3t
    @DIVYPAREEK-v3t ปีที่แล้ว +1

    this is the best lecture so far

  • @alvinaawan884
    @alvinaawan884 4 ปีที่แล้ว +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

  • @cainmorano4956
    @cainmorano4956 10 หลายเดือนก่อน +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.

  • @lightcapmath2777
    @lightcapmath2777 3 ปีที่แล้ว

    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 ปีที่แล้ว +3

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

  • @stalins1383
    @stalins1383 7 ปีที่แล้ว +25

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

  • @RC-bm9mf
    @RC-bm9mf 5 ปีที่แล้ว

    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 ปีที่แล้ว

      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.

  • @funghang3482
    @funghang3482 6 ปีที่แล้ว +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 .

  • @IMadeOfClay
    @IMadeOfClay 8 หลายเดือนก่อน +3

    4:30: Professor Strang was brutal on a3 😂

  • @ahmedkhalifa9333
    @ahmedkhalifa9333 2 ปีที่แล้ว

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

  • @DrChillg00d
    @DrChillg00d 5 ปีที่แล้ว +1

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

  • @arjunag7553
    @arjunag7553 10 หลายเดือนก่อน

    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 ปีที่แล้ว

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

  • @omkarkhare9160
    @omkarkhare9160 6 ปีที่แล้ว +2

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

  • @Googk
    @Googk 3 ปีที่แล้ว

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

  • @ComfyDyl
    @ComfyDyl ปีที่แล้ว

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

  • @georgesadler7830
    @georgesadler7830 3 ปีที่แล้ว +1

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

  • @andizvlogs
    @andizvlogs 6 ปีที่แล้ว

    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.

  • @samarathrodriguez7662
    @samarathrodriguez7662 7 ปีที่แล้ว +8

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

  • @deadbutworking
    @deadbutworking 4 ปีที่แล้ว +1

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

  • @xblockitv
    @xblockitv 5 ปีที่แล้ว

    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.

  • @falconlin419
    @falconlin419 ปีที่แล้ว

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

  • @AyushBhattfe
    @AyushBhattfe 7 ปีที่แล้ว +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 ปีที่แล้ว

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

  • @WestOfEarth
    @WestOfEarth 5 ปีที่แล้ว

    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.

  • @EsKaioS
    @EsKaioS 6 ปีที่แล้ว

    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 ปีที่แล้ว +1

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

  • @Aventinium
    @Aventinium 9 หลายเดือนก่อน

    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.

  • @NothingMaster
    @NothingMaster 5 ปีที่แล้ว +1

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

  • @ianbridges6040
    @ianbridges6040 3 ปีที่แล้ว

    Thank you MIT OCW and Dr. Strang!

  • @khushaalnandwani3372
    @khushaalnandwani3372 4 ปีที่แล้ว

    Subspace explained beautifully at @8:00

  • @dabeeramir1407
    @dabeeramir1407 ปีที่แล้ว

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

  • @vrclckd-zz3pv
    @vrclckd-zz3pv 2 ปีที่แล้ว

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

  • @laurencealanano2495
    @laurencealanano2495 3 ปีที่แล้ว

    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.

  • @michaeltheisen
    @michaeltheisen 2 ปีที่แล้ว

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

  • @srirampallav2765
    @srirampallav2765 4 ปีที่แล้ว

    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.

  • @benrow5472
    @benrow5472 6 ปีที่แล้ว +1

    you're the man Gilbert Strang.

  • @dhrubajyotipaul8204
    @dhrubajyotipaul8204 ปีที่แล้ว

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

  • @Synconntez
    @Synconntez 4 ปีที่แล้ว +2

    This guy CAN TEACH!

  • @douglasvargasdasilva7537
    @douglasvargasdasilva7537 6 ปีที่แล้ว

    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.

  • @dtalmood
    @dtalmood 5 ปีที่แล้ว +1

    This guy is the real MVP

  • @Sky-pg6xy
    @Sky-pg6xy 5 ปีที่แล้ว

    His voice makes learning Linear Algebra fun

  • @danieladeba206
    @danieladeba206 3 ปีที่แล้ว

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

  • @makuwaniblessing743
    @makuwaniblessing743 4 ปีที่แล้ว

    2020 and you are still good proff

  • @TonyTorzido
    @TonyTorzido 3 ปีที่แล้ว

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

  • @nora-xk6gv
    @nora-xk6gv 7 ปีที่แล้ว +1

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

  • @publicplace2034
    @publicplace2034 ปีที่แล้ว +1

    It's Amazing sir,

  • @jamesgreat5263
    @jamesgreat5263 2 หลายเดือนก่อน

    Damn that's in MIT, this was gold

  • @royah5404
    @royah5404 8 ปีที่แล้ว +14

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

    • @ahsan400
      @ahsan400 7 ปีที่แล้ว +8

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

  • @MohamedAhmed-fq6yy
    @MohamedAhmed-fq6yy 3 ปีที่แล้ว

    I wanna hug this man

  • @sunnyvishnoi4310
    @sunnyvishnoi4310 ปีที่แล้ว

    Wow! What a brilliant explanation. Living legend❤

  • @damiantoddwell5439
    @damiantoddwell5439 6 ปีที่แล้ว

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

  • @stevenshi9012
    @stevenshi9012 3 ปีที่แล้ว

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

  • @jas_n1580
    @jas_n1580 4 ปีที่แล้ว

    This man is such a treasure! Great lecture

  • @somenn.s3977
    @somenn.s3977 3 ปีที่แล้ว

    Only depressing thing is that Prof.Strang is getting old ,wished he were half of his present age ,more gems from math we can get.

  • @kanikabagree1084
    @kanikabagree1084 4 ปีที่แล้ว

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

  • @d.n.aengineering1485
    @d.n.aengineering1485 6 ปีที่แล้ว

    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

  • @ruskodudesko9679
    @ruskodudesko9679 7 ปีที่แล้ว

    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.

  • @arijeong9946
    @arijeong9946 3 ปีที่แล้ว

    7:05 basis

  • @centerfield6339
    @centerfield6339 หลายเดือนก่อน +1

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

  • @distilledleemupaani9232
    @distilledleemupaani9232 4 ปีที่แล้ว

    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 ปีที่แล้ว

      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

  • @zombie-blood-490gaming5
    @zombie-blood-490gaming5 5 ปีที่แล้ว +3

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

  • @pragmatic_p8
    @pragmatic_p8 4 หลายเดือนก่อน

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

  • @100yearsofsolitudful
    @100yearsofsolitudful 7 ปีที่แล้ว

    ive never had it explained so well like this, thanks

  • @AjayKumar-zq7vm
    @AjayKumar-zq7vm 6 ปีที่แล้ว +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

  • @kaiserluvsmariel
    @kaiserluvsmariel 4 ปีที่แล้ว

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

  • @karangujarati4589
    @karangujarati4589 5 ปีที่แล้ว +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 🤟🏻

  • @trading_denial
    @trading_denial 4 ปีที่แล้ว +1

    Many many thanks for your good explanation!!

  • @simonthomas5848
    @simonthomas5848 5 ปีที่แล้ว +1

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

  • @letlhogonolonape849
    @letlhogonolonape849 7 ปีที่แล้ว +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

  • @stewartmoore5158
    @stewartmoore5158 5 ปีที่แล้ว

    A true math hero.

  • @akashverma1640
    @akashverma1640 6 ปีที่แล้ว

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

  • @josephrussell1419
    @josephrussell1419 2 หลายเดือนก่อน

    I'm not sure if the captions are auto-generated. They keep reading "our three" instead of "R^3"

    • @mitocw
      @mitocw  2 หลายเดือนก่อน

      Thanks for your note! No, the captions are not auto-generated. We've updated the captions.

  • @madiganrios8865
    @madiganrios8865 ปีที่แล้ว

    Good video, thank you. I find this stuff really confusing and this really cleared things up

  • @rohhthone
    @rohhthone 11 หลายเดือนก่อน

    I loved his videos! Where I can find more?

    • @mitocw
      @mitocw  11 หลายเดือนก่อน

      Here's the playlist for this resource: th-cam.com/play/PLMsYJgjgZE8iBpOBZEsS8PuwNBkwMcjix.html. Here's all the courses we have by Gil: ocw.mit.edu/search/?q=%22Prof.%20Gilbert%20Strang%22. Best wishes on your studies!

  • @lolnets5832
    @lolnets5832 5 ปีที่แล้ว

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

  • @Humble.fool05
    @Humble.fool05 6 ปีที่แล้ว

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

  • @Michael-ud4wr
    @Michael-ud4wr 8 ปีที่แล้ว +12

    This guy is great

    • @denizerol1
      @denizerol1 4 ปีที่แล้ว

      not like that 6 3 5 that guy is a loser

  • @munipradeep3314
    @munipradeep3314 6 ปีที่แล้ว

    Super neat with microscopic clarity

  • @abhisheksingha8008
    @abhisheksingha8008 2 ปีที่แล้ว +1

    😔 ....... Please upload full video cource in TH-cam or any site for those student who not get chance in MiT but want good concept with Clearity...