Independence, Basis, and Dimension

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

[@valeriereid2337]

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

[@doyochi02]

lol I'm about to say that

[@Ztingjammer]

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

[@jmr218]

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

[@vladkovalenko9222]

True)

[@RazorM97]

I so agree, wow

[@HK-sw3vi]

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

[@calvinmata56]

@@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]

In which college u r ??

[@SilverArro]

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]

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

[@mikem9270]

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

[@RutwikGulakala]

@@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]

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]

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

[@dheerajsharma224]

same bro

[@divutiful]

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.

[@water7875]

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

[@chandrapandey822]

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

[@chandrapandey822]

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

[@josephgeorge2513]

Can you email me the pdf or direct me to it

[@monaal.8494]

What is the name of his book please!

[@emma.muhleman]

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

[@vongxiong5125]

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

[@ankur7041]

1,0,0 What the heck!

[@diy-projects]

*than*

[@truthalonetriumphs6572]

He’s an American professor :)

[@rickeyaustin7649]

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!

[@stalins1383]

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

[@ragsiruh]

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

[@alvinaawan884]

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

[@johnxiaoyuzhang8961]

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

[@lightcapmath2777]

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:)

[@jwyliecullick8976]

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.

[@vocdex]

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

[@farrugiamarc0]

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.

[@ruskodudesko9679]

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.

[@user-cc4zj4mv9u]

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

[@falconlin419]

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

[@omkarkhare9160]

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

[@LICHKING55Show]

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.

[@ahmedkhalifa9333]

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

[@letlhogonolonape849]

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

[@CocoGras]

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

[@laurencealanano2495]

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.

[@srirampallav2765]

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.

[@zhaomike952]

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

[@andizvlogs]

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.

[@karangujarati4589]

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

[@dabeeramir1407]

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

[@EsKaioS]

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

[@douglasvargasdasilva7537]

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.

[@damiantoddwell5439]

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

[@d.n.aengineering1485]

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

[@funghang3482]

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]

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

[@ianbridges6040]

Thank you MIT OCW and Dr. Strang!

[@nora-xk6gv]

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

[@ComfyDyl]

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

[@byomkeshbabu]

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

[@honkhonk8009]

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

[@erickhumalo1913]

You're a Legend Madala Thank you so much

[@100yearsofsolitudful]

ive never had it explained so well like this, thanks

[@dhrubajyotipaul8204]

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

[@danieladeba206]

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

[@akashverma1640]

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

[@benrow5472]

you're the man Gilbert Strang.

[@vrclckd-zz3pv]

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

[@EdorahVtuber]

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

[@souvikcseiitk]

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

[@kanikabagree1084]

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

[@matheuscardoso1110]

thank you very much for all your teachings!!! much love from Brazil!

[@jas_n1580]

This man is such a treasure! Great lecture

[@stevenshi9012]

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

[@royah5404]

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

[@ahsan400]

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

[@samarathrodriguez7662]

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

[@arjunag7553]

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

[@georgesadler7830]

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

[@phenotypealpha]

Gilbert you are a lifesaver much love!

[@user-qe7cw3tr1e]

this is the best lecture so far

[@suryanshshukla7384]

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

[@avigautam6735]

Bmte 141?

[@munipradeep3314]

Super neat with microscopic clarity

[@makuwaniblessing743]

2020 and you are still good proff

[@steve8219]

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

[@alhaithamaljabri2203]

You are an amazing professor!

[@alexiadrey938]

Wow, just wow. Wonderful professor. Thank you:)

[@AjayKumar-zq7vm]

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

[@trading_denial]

Many many thanks for your good explanation!!

[@sunnyvishnoi4310]

Wow! What a brilliant explanation. Living legend❤

[@Lena-wn2lg]

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

[@simonthomas5848]

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

[@kaiserluvsmariel]

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

[@WestOfEarth]

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.

[@lolnets5832]

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

[@AyushBhattfe]

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

[@Sky-pg6xy]

His voice makes learning Linear Algebra fun

[@aprillam227]

super cool. such a life saver for my exam!

[@cainmorano4956]

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.

[@xyz-qe1vu]

Simply amazing. Simple and amazing.

[@Synconntez]

This guy CAN TEACH!

[@mrxinnovations809]

phenomenal lecture !!

[@arthurabreu3736]

Thank you professor. You are amazing.

[@TonyTorzido]

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

[@AryanPatel-wb5tp]

what a great professor !

[@MohamedAhmed-fq6yy]

I wanna hug this man

[@anqiwen6997]

Thank you, Professor!

[@AjaySaini-zp5cg]

What a great professor.......... Man

[@4subvoid4]

Excellent teacher!

[@edyraper]

Thanks for explaining this. I get the idea in first 2 minnutes. It's really a service to humanity.

[@madiganrios8865]

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

[@reinia127]

thank you so much !!! finally I understand what span means

[@Ambu_Singh]

Incredible lecture

[@liemh9290]

Clear. Precise.

[@Michael-ud4wr]

This guy is great

[@denizerol1]

not like that 6 3 5 that guy is a loser

[@rohithperumandla4302]

Really awesome explanation sir

[@logio7663]

I wish I could learn from him everyday

[@priyankar.5620]

Very nicely explained.

[@saiouln.8060]

Amazing prof!!

[@erwinjedracho640]

have to learn it from the master and from the best