Independence, Basis, and Dimension

  Рет қаралды 396,413

MIT OpenCourseWare

MIT OpenCourseWare

8 жыл бұрын

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: ocw.mit.edu/RES-18-009F15
Instructor: Gilbert Strang
Vectors are a basis for a subspace if their combinations span the whole subspace and are independent: no basis vector is a combination of the others. Dimension = number of basis vectors.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

Пікірлер: 283
@valeriereid2337
@valeriereid2337 3 жыл бұрын
I am certainly glad to see a professor who teaches from his brain, not reading from power point slides. This is refreshing.
@doyochi02
@doyochi02 Жыл бұрын
lol I'm about to say that
@Ztingjammer
@Ztingjammer Жыл бұрын
It most certainly is! It's so captivating as well.
@jmr218
@jmr218 7 жыл бұрын
Wow, the first 2 minutes of this lecture explain the topics better than 1.5 hours listening to my current teachers.
@vladkovalenko9222
@vladkovalenko9222 5 жыл бұрын
True)
@RazorM97
@RazorM97 4 жыл бұрын
I so agree, wow
@HK-sw3vi
@HK-sw3vi 4 жыл бұрын
you weren't paying attention in the class, let's be real
@calvinmata56
@calvinmata56 4 жыл бұрын
@@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 жыл бұрын
In which college u r ??
@SilverArro
@SilverArro 8 жыл бұрын
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 жыл бұрын
Arlo I wouldn’t say crystal clear in my opinion.
@mikem9270
@mikem9270 5 жыл бұрын
@@lucasm4299 compared to my professor, clearer than crystal XD ... My professor shouldnt be allowed teach
@RutwikGulakala
@RutwikGulakala 5 жыл бұрын
@@mikem9270 I agree. My professor couldn't explain what Dependent and Independent vectors are properly and every student in the class lost their shit.
@cristinabosch
@cristinabosch 5 жыл бұрын
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 6 жыл бұрын
Man... Wish my linear Algebra classes were as half as good as this one... This is simply beautiful.
@dheerajsharma224
@dheerajsharma224 2 жыл бұрын
same bro
@divutiful
@divutiful 3 жыл бұрын
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.
@vongxiong5125
@vongxiong5125 6 жыл бұрын
1,0,0 is a better A3... then.. that loser, that 6,3,5. LOL he's halarious.
@ankur7041
@ankur7041 4 жыл бұрын
1,0,0 What the heck!
@diy-projects
@diy-projects 4 жыл бұрын
*than*
@truthalonetriumphs6572
@truthalonetriumphs6572 4 жыл бұрын
He’s an American professor :)
@water7875
@water7875 7 жыл бұрын
This dude wrote the text book im referring for linear algebra! His lectures are as amazing as his book!
@chandrapandey822
@chandrapandey822 6 жыл бұрын
mustard seed Yup and most importantly it talks abt. the APPLICATIONS which is more important.
@chandrapandey822
@chandrapandey822 6 жыл бұрын
mustard seed But sadly I have the book in PDF format..
@josephgeorge2513
@josephgeorge2513 5 жыл бұрын
Can you email me the pdf or direct me to it
@monaal.8494
@monaal.8494 5 жыл бұрын
What is the name of his book please!
@emma.muhleman
@emma.muhleman 4 жыл бұрын
I WANT HIS BOOK! Expensive though, you can't get it free, right?
@rickeyaustin7649
@rickeyaustin7649 7 жыл бұрын
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!
@ragsiruh
@ragsiruh 5 жыл бұрын
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
@johnxiaoyuzhang8961
@johnxiaoyuzhang8961 Жыл бұрын
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
@jwyliecullick8976
@jwyliecullick8976 4 жыл бұрын
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.
@alvinaawan884
@alvinaawan884 3 жыл бұрын
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
@vocdex
@vocdex 5 жыл бұрын
Thanks to Dr Strang, I can now visualize what does all concepts represent. The things are very clear right now.
@stalins1383
@stalins1383 7 жыл бұрын
You are amazing sir... Education is all about transferring your intuition to others... You always great in that.
@farrugiamarc0
@farrugiamarc0 8 ай бұрын
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 4 жыл бұрын
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.
@lightcapmath2777
@lightcapmath2777 3 жыл бұрын
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:)
@user-cc4zj4mv9u
@user-cc4zj4mv9u 2 жыл бұрын
My deepest respect to Professor Strang. Respect to his perennial enthusiasm, and all those years he had devoted to his field.
@omkarkhare9160
@omkarkhare9160 6 жыл бұрын
such an awesome guy! That's how math should be taught! You can never get bored while hearing Dr Strang's lectures..
@ahmedkhalifa9333
@ahmedkhalifa9333 2 жыл бұрын
One like is certainly not enough for your enthusiasm and dedication Prof. Strang.
@ruskodudesko9679
@ruskodudesko9679 6 жыл бұрын
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.
@zhaomike952
@zhaomike952 3 жыл бұрын
The best professor I've ever seen. There is the MIT!
@falconlin419
@falconlin419 Жыл бұрын
You're the best, professor. I am studying from the 18.06 in spring 2010 and you explain everything very clear. Thank you!
@funghang3482
@funghang3482 6 жыл бұрын
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 .
@deadbutworking
@deadbutworking 3 жыл бұрын
God what a godsend .. been trying to get these simple concepts for so long and finally one video did it!
@laurencealanano2495
@laurencealanano2495 3 жыл бұрын
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.
@andizvlogs
@andizvlogs 6 жыл бұрын
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.
@dabeeramir1407
@dabeeramir1407 7 ай бұрын
Amazingly explained, I've been trying to figure out this stuff for so long and you explained it beautifully
@ComfyDyl
@ComfyDyl 7 ай бұрын
you are a legend, this is so much more clear than any other explanations ive seen
@steve8219
@steve8219 4 жыл бұрын
Oh god, I paid $6000 for a Maths course in uni and barely understand teacher talking about, and it turns out free KZbin video helped me understand every single concept. Imao
@srirampallav2765
@srirampallav2765 4 жыл бұрын
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.
@damiantoddwell5439
@damiantoddwell5439 5 жыл бұрын
Thank you professor.. Now i have finally understood something that has been puzzling me for a week..
@souvikcseiitk
@souvikcseiitk Жыл бұрын
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
@EsKaioS
@EsKaioS 5 жыл бұрын
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
@letlhogonolonape849
@letlhogonolonape849 6 жыл бұрын
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
@arjunag7553
@arjunag7553 4 ай бұрын
Been wracking my brain for two days..listened to one line of his explanation and I got all the clarity in the world.
@karangujarati4589
@karangujarati4589 4 жыл бұрын
So good to hear and learn from u sir, Clear my fundamental about dimensions and basis very well. Yup better than hours of class 🤟🏻
@nora-xk6gv
@nora-xk6gv 6 жыл бұрын
you deserve the whole respect Prof I would like to thank you so much .
@CocoGras
@CocoGras 4 жыл бұрын
Thank you so much for sharing these lectures-- You've helped me so much!! Pure love!!
@samarathrodriguez7662
@samarathrodriguez7662 6 жыл бұрын
Every time I watch Strang's videos everything makes so much sense and I wonder why I hate Linear Algebra so much.
@honkhonk8009
@honkhonk8009 Жыл бұрын
god i love this guy. hes so chill bro. Explained everything perfectly. Damn
@ianbridges6040
@ianbridges6040 2 жыл бұрын
Thank you MIT OCW and Dr. Strang!
@douglasvargasdasilva7537
@douglasvargasdasilva7537 6 жыл бұрын
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.
@100yearsofsolitudful
@100yearsofsolitudful 7 жыл бұрын
ive never had it explained so well like this, thanks
@byomkeshbabu
@byomkeshbabu 6 жыл бұрын
Finally got the idea of basis right. Thanks, Prof Strang!
@benrow5472
@benrow5472 6 жыл бұрын
you're the man Gilbert Strang.
@d.n.aengineering1485
@d.n.aengineering1485 6 жыл бұрын
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
@dhrubajyotipaul8204
@dhrubajyotipaul8204 Жыл бұрын
This was so simply explained that I'm in tears. THANK YOUUUU!!! ♥♥♥
@Lena-wn2lg
@Lena-wn2lg 9 ай бұрын
Professor Strang is a genius math teacher!! This is how math should be taught.
@EdorahVtuber
@EdorahVtuber 4 жыл бұрын
omfg i love this guy and his explanations actually make sense!
@AyushBhattfe
@AyushBhattfe 6 жыл бұрын
I read the book, then I come to Strang's lectures and I am always all like "oh wtf, yeah it makes sense now"
@kanikabagree1084
@kanikabagree1084 4 жыл бұрын
Best teacher i've come across thankyou so much for saving us 😭
@akashverma1640
@akashverma1640 6 жыл бұрын
This video cleared all the ambiguities of mine related to these terms a big thanks to Sir....
@erickhumalo1913
@erickhumalo1913 4 жыл бұрын
You're a Legend Madala Thank you so much
@vrclckd-zz3pv
@vrclckd-zz3pv 2 жыл бұрын
This video provided me with a very Strang introduction to the concepts. Thank you.
@jas_n1580
@jas_n1580 3 жыл бұрын
This man is such a treasure! Great lecture
@cainmorano4956
@cainmorano4956 4 ай бұрын
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.
@stevenshi9012
@stevenshi9012 3 жыл бұрын
thank you! Dr. Strang. You invoke my interest in math as a math student!
@georgesadler7830
@georgesadler7830 2 жыл бұрын
These topics are important in linear algebra. DR. Strang explains these topics very well in the video.
@user-qe7cw3tr1e
@user-qe7cw3tr1e 11 ай бұрын
this is the best lecture so far
@danieladeba206
@danieladeba206 2 жыл бұрын
Wow!I have never seen such like lecturer....amazing, brilliant for sure!!
@matheuscardoso1110
@matheuscardoso1110 5 жыл бұрын
thank you very much for all your teachings!!! much love from Brazil!
@phenotypealpha
@phenotypealpha 5 жыл бұрын
Gilbert you are a lifesaver much love!
@WestOfEarth
@WestOfEarth 4 жыл бұрын
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.
@makuwaniblessing743
@makuwaniblessing743 3 жыл бұрын
2020 and you are still good proff
@Sky-pg6xy
@Sky-pg6xy 4 жыл бұрын
His voice makes learning Linear Algebra fun
@lolnets5832
@lolnets5832 5 жыл бұрын
this is a man of the people....congrats
@AjayKumar-zq7vm
@AjayKumar-zq7vm 6 жыл бұрын
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
@DrChillg00d
@DrChillg00d 5 жыл бұрын
5 sections of gibberish laid out in 13 totally crystal clear minuets. good lord this is magic
@kaiserluvsmariel
@kaiserluvsmariel 3 жыл бұрын
You're an angel sent from heaven! Thank you so much for these wonderful videos!!!
@suryanshshukla7384
@suryanshshukla7384 2 жыл бұрын
This is best explaination i have listen for basis, dimension and subspace. It explains everything with connecting one idea to another.
@avigautam6735
@avigautam6735 Жыл бұрын
Bmte 141?
@TonyTorzido
@TonyTorzido 2 жыл бұрын
Bruh what a G. He made it super easy. Thanks, profe
@munipradeep3314
@munipradeep3314 5 жыл бұрын
Super neat with microscopic clarity
@simonthomas5848
@simonthomas5848 4 жыл бұрын
I love you sir!!! you are a healer!
@alhaithamaljabri2203
@alhaithamaljabri2203 6 жыл бұрын
You are an amazing professor!
@aprillam227
@aprillam227 5 жыл бұрын
super cool. such a life saver for my exam!
@sunnyvishnoi4310
@sunnyvishnoi4310 9 ай бұрын
Wow! What a brilliant explanation. Living legend❤
@royah5404
@royah5404 7 жыл бұрын
explained very well. wish he is my professor! thank you!
@ahsan400
@ahsan400 7 жыл бұрын
He is your professor. Aren't you studying from him? If yes, then he is :)
@Aventinium
@Aventinium 4 ай бұрын
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.
@alexiadrey938
@alexiadrey938 3 жыл бұрын
Wow, just wow. Wonderful professor. Thank you:)
@MohamedAhmed-fq6yy
@MohamedAhmed-fq6yy 3 жыл бұрын
I wanna hug this man
@edyraper
@edyraper 6 жыл бұрын
Thanks for explaining this. I get the idea in first 2 minnutes. It's really a service to humanity.
@zombie-blood-490gaming5
@zombie-blood-490gaming5 5 жыл бұрын
god bless you sir, i havent understood this this shit for 3 months till i found this video!
@RC-bm9mf
@RC-bm9mf 4 жыл бұрын
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 4 жыл бұрын
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.
@Synconntez
@Synconntez 3 жыл бұрын
This guy CAN TEACH!
@mainmuhammadramzan
@mainmuhammadramzan 5 жыл бұрын
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.
@NothingMaster
@NothingMaster 5 жыл бұрын
“That loser 6, 3, 5” 😂 Strang is an exceptionally gifted lecturer And an absolute straight-faced blast. LOL
@logio7663
@logio7663 6 жыл бұрын
I wish I could learn from him everyday
@xyz-qe1vu
@xyz-qe1vu 3 жыл бұрын
Simply amazing. Simple and amazing.
@madiganrios8865
@madiganrios8865 8 ай бұрын
Good video, thank you. I find this stuff really confusing and this really cleared things up
@jkim9931
@jkim9931 3 жыл бұрын
9:55 dimension = # of basis vectors for the subspace
@trading_denial
@trading_denial 3 жыл бұрын
Many many thanks for your good explanation!!
@AjaySaini-zp5cg
@AjaySaini-zp5cg 5 жыл бұрын
What a great professor.......... Man
@erwinjedracho640
@erwinjedracho640 7 жыл бұрын
have to learn it from the master and from the best
@Googk
@Googk 2 жыл бұрын
Subspace: không gian con Basis: cơ sở của vectơ Column: cột Dimension: số chiều
@reinia127
@reinia127 5 жыл бұрын
thank you so much !!! finally I understand what span means
@AryanPatel-wb5tp
@AryanPatel-wb5tp 3 ай бұрын
what a great professor !
@ravikumar.8763
@ravikumar.8763 4 жыл бұрын
Thank you so much Professor, now my confusion on this point is "crystal clear " This was a marvelous & interesting lecture. Thnx once again...
@arthurabreu3736
@arthurabreu3736 Жыл бұрын
Thank you professor. You are amazing.
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