Gil Strang's Final 18.06 Linear Algebra Lecture

Speakers: Gilbert Strang, Alan Edelman, Pavel Grinfeld, Michel Goemans
Revered mathematics professor Gilbert Strang capped a 61-year career as a faculty member at MIT by delivering his final 18.06 Linear Algebra lecture before retiring at the age of 88. In addition to a brief review for the course final exam, the overflowing audience (both in person and on the live KZbin stream) heard recollections, appreciations, and congratulations from Prof. Strang’s colleagues and former students. A rousing standing ovation concluded this historic event.
0:00 - Seating
8:56 - Class start
10:05 - Alan Edelman's speech about Gilbert Strang
12:57 - Gilbert Strang's introduction
15:42 - Solving linear equations
30:42 - Visualization of four-dimensional space
31:37 - Nonzero Solutions
32:16 - Finding Solutions
34:19 - Elimination Process
41:05 - Introduction to Equations
42:26 - Finding Solutions
44:29 - Solution 1
47:42 - Rank of the Matrix
51:39 - In appreciation of Gilbert Strang
52:08 - Congratulations on retirement
52:38 - Personal experiences with Strang
55:01 - Life lessons learned from Strang
1:01:08 - Gil Strang's impact on math education
1:01:44 - Gil Strang's teaching style
1:02:20 - Gil Strang's legacy
1:03:23 - Congratulations to Gil Strang
This video has been dubbed using an artificial voice via aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu.
License: Creative Commons BY-NC-SA
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[@johnstrang9300]

Posted on behalf of Gil Strang: This is my chance to thank everyone for such generous messages about my last lecture at MIT. I am almost tempted to have second thoughts about retirement ....... but it is the right time. Teaching has been a wonderful life. And I am so grateful to everyone who likes linear algebra and sees its importance. So many universities ( and even high schools ) now appreciate how beautiful it is and how valuable it is. That movement will continue because it is right. I thank you for your good thoughts. I appreciate them more than I can say. Very best wishes in all your work Gil

[@ldx8492]

Heartfelt 😭

[@ArchimedesBC]

"Tempted to have second thoughts about retirement"? Please don't retire!

[@gabrielbarberini9846]

Strang, thank you so much! We owe you years of joy for such inspiring lectures and books, never to be forgotten. Best regards from Brazil

[@marccox8977]

I Love Gil's enthusiasm! And appreciate his brilliant insights and tricks of the trade with Matrix decompositions e.g. SVD , LU etc. - just when you think "it's all been done" BOOM Gil nails a new one! Ps> Long live Gil, Long live Linear Algebra, Long live the Julia language! 👍😁👍

[@solarion33]

there is always the prospect of doing more KZbin video's from the comfort of your home , living the KZbin life :-)

[@vplay2619]

what a legend retired after 61 years of teaching at MIT . RESPECT 🙌👏👏

[@seanli3757]

He's still as interesting as he was young

[@anoopramakrishna]

63

[@mahdiehebrahimi3612]

​@@seanli3757 😮😮😮😊😊😊

[@user-si7sw7xy4n]

OK

[@user-si7sw7xy4n]

無超過易經

[@juliogaleano2063]

Professor Strang I had the honor of attending your lectures back in 1986 as a graduate student at MIT and it was such a wonderful and enlightening experience. You signed me a very kind dedication in your book that I will always treasure. I never forgot you and I never will. I wish you the very best

[@sam-avni]

So are you retired now? What you did after your graduation?

[@juliogaleano2063]

@@sam-avni I taught in Argentina my native country for many years in the area of computer science and FEM not algebra. Why?

[@puneettripathi740]

​​@@juliogaleano2063I believe he was curious sir, the way we all are about stories that we come across in life. I personally believe you did a fantastic job by teaching people in your country I really admire that and thank u for your services ❤

[@juliogaleano2063]

@@puneettripathi740 thank you very much for your kind words. Where are you from?

[@puneettripathi740]

@@juliogaleano2063 I am from Bharat sir.😊🙏

[@katarixy]

I had to pay for college out of my own pocket, without any financial aid, I had three part time jobs and little room to sleep. I used to watch videos to go to sleep (math and Physics primarily). I remember watching the Strang's linear algebra series before I took the class myself. I went on to get a perfect in the class and I cannot help but feel so grateful to all his work and dedication. Thank you!!!

[@katarixy]

@@b0benis linear algebra is a common class all math majors have to take at all schools...

[@mysteriousshadow395]

No financial aid? I think most unis will give need-based aid regardless, no?

[@zelousfoxtrot3390]

@@mysteriousshadow395 Not if your parents make $$$ and don't share. Can't qualify for low interest loans then either. And loans aren't truly financial aid- they are a noose. Perhaps they were trying to keep the debt down? I've had more than one friend who was utterly screwed from '18 and you're out' parents.

[@Mark-nm9sm]

@@b0benis i think maybe he means he went to an other unviersity with lower fees and just watched strang's videos before attending the linear algebra class at that other university

[@tysontakayushi8394]

@@b0benis in the USA maybe

[@shinehitcs]

GIl's lecture was probably the first time I realized the difference between MIT and other universities.

[@wuzhai2009]

It is the difference between Prof. Strang and other universities.

[@ivandavidrodriguezamezquit2402]

no

[@aNotoriousPhD]

strang is great, but i think that’s speaking a bit too broadly to categorize MIT that way

[@HikarusVibrator]

Were you at all “the other” universities? He’s a legend, but there are exceptional lecturers in may parts of the world.

[@anthonygaertner8749]

@HikariOfficialSoutjAfricaFanclub do you mind recommending some please

[@user-dg8xq3jz7z]

Professor Strang's Linear Algebra Lecture is a real treasure. May Professor Strang has a wonderful retire life! Salute.

[@jwshao8915]

黑手哥也学线代啊

[@newhouse8867]

头像真没绷住

[@user-dg8xq3jz7z]

​@@jwshao8915 Do you dare to bihuabihua with me?

[@xtzhao2196]

​@@user-dg8xq3jz7z small puxxy cub

[@danypell2517]

He was already retired. To him, it is passion. :) he's almost 90!

[@ReveredDead]

61 freaking years?! Holy crap....he's been teaching longer than my own dad has been alive.

[@mohammadshahadathhossain981]

An entire generation of linear algebra learners will be indebted to you professor Strang. Heartfelt thanks for your passion towards the subject. Wishing you a great retirement life with your nearest and the dearest ones. Also, a big big thanks to MIT for being so generous in making these priceless video lectures available for the students worldwide!

[@toseefkhan921]

What great he did so he will be remembered? Can y tell me

[@JohnSmith-xx9th]

You’re praising him like he’s some kind of god 😂

[@Mark-nm9sm]

@@JohnSmith-xx9th he is higher than god, his teachings are based on logic not fairytales

[@joducringe]

​@@toseefkhan921difference bw a professor and an uneducated kid

[@jihadalsweed]

I teared up watching him say thank you at the end. we all wish we could accomplish something in life that is appreciated for years, and gilbert strang did more than that, and inspired thousands of people to purse math, study the subject, and teach others.

[@fredirecko]

millions

[@abhisheksoni9774]

Well said 👏

[@unclefreddy2009]

I’m so grateful to live in a time when I can be exposed to this level of understanding and teaching. I struggled through linear algebra in college and here I am 30 years later watching this- learning from someone who I only wish I could have had as a professor. Thank you professor, the world is a better place with you in it

[@gongfei]

I failed my linear algebra course. Then, learned it again from professor Strang's lecture here on youtube.

[@kenfrank2730]

I wish I had this video back when I took linear algebra. The teacher I had was so bad he couldn't teach a dog to roll over.

[@thispersonwriting1889]

Without Gilbert Strang’s lectures, I wouldn’t have been able to graduate. From the bottom of my heart, thank you.

[@TheVeritas2100]

DITTO likely hundreds like you ... as an engineering student in 1960's I have 'blitzed' the Linear Algebra course ( many have not ... LOL! ) - but when I discoverd Gilbert Strang at MIT on line ( likely in the late 90's I think) - and I decided to 'amuse' myseslf, even though I have left engineering and math world in the mid-1970's, and to my great AMAZEMENT I found out that, as an undegrad, I actually I never fully undestood the Linear Algebra ! WHAT AN AMAZING LECTURER ! Sadly, the universities now focus on 'diversity', 'euality' and other dumb NON-SENSE, and the STEM America's much behind the world , by a light year !

[@thispersonwriting1889]

@@TheVeritas2100 Your comment made me realize that Prof. Strang’s use of the internet as an archive of his teaching lasted decades. Truly a farsighted man, ahead of his time. (As for your last paragraph, let’s try to keep things lighthearted and congratulatory, we’re here to celebrate Professor Strang, not to criticize other academics).

[@TheVeritas2100]

@@thispersonwriting1889 ****as for YOUR last paragraph**** - IT IS VERY SAD THAT The Harvards, The Yales , etc. are now DESTROYING the great American Universities culture , with the LGBTQFU2plus and other WOKEness crap ... 😞 - when they are appointing the LGBTQU2plus Presidents who are are cheaters, not qualified, dumb, plagiarsers, and/or political hacks - INSTEAD OF THE REAL QUALITY PROFESSIONAL ACADEMICS !!!!

[@mdrayhanuddinmojumder]

87 years old man teaching with such clarity. Remarkable! Unbelievable! Madness!! Thank you, Mr Gilbert. You help me to transition from Biology undergrad to physics . I will forever be indebted to you. I rediscovered my love for mathematics from you. You sir, are a legend of a kind. I love my life now. Thank you so much.

[@sgravina]

I thought Professor Strang's course was great when I took it in 1998. I still have his book. And I was a working physicist then that already knew linear algebra and used it. He brought out the coolness of matrix algebra. Which I still have. Professor Strang is my mother's age. She passed 20 years ago and I retired 4 years ago. It's fun to see someone who likes what they do enough to work at it forever.

[@harshpatel4431]

It's his ikigai

[@quentin2578]

You must have done well if you retired 21 years after your college period, even if you were already working; good for you!

[@sgravina]

@@quentin2578 I was 40 years old when I took the course. I was working at an MIT laboratory and the course was free for me. I heard it was a good course and the timing was convenient. Honestly, I didn't need any of it and it didn't change anything about how I used linear algebra but it was still cool to hear Strang's presentation. So I sat through the whole semester.

[@quentin2578]

@@sgravina Thanks for your genuine reply. Even though you were acquainted with the theory, it must have been a great and/or memorable experience to be in that environment during the personal computer/e-mail/internet technology revolution, right? Especially when surrounded with lecturers that have great analogies to better teach one math and physics. I may have a distorted view. I am an eighteen-year-old student from the Netherlands and could not dream of a better time to be in college then during those days. No social media, a lot of face-to-face communication or simply telephone calls, studying entirely via books and libraries; man, I wish I was there.

[@LinoCoriaCisneros]

Being an old teacher myself, Professor Strang always was my OCW indispensable teacher and a roll model to anyone in our profesion. I met personaly Dr. Strang in a meeting in Morelia, Mexico long time ago, and i was touched for his kindness. Hope you'll have a long and happy life. I can't say enough how much I thank you

[@kewkabe]

I had Prof. Strang for 18.06 in '88 and it was one of my favorite classes at MIT, thanks to him!

[@ShifutheNomad]

He taught my friend, his daughter, and her son. Three generations had the pleasure of being taught by this brilliant man. ❤

[@alisharifi8917]

Dear Prof. Stang, as a faculty member of AI in Sharif University of Technology (Iran) I wanted to express my deep admiration for your linear algebra course, which I thoroughly enjoyed and have enthusiastically recommended to my students. Teaching math in a way that instills a love for the subject is a challenging task, much harder than solving complex equations. But your teaching style effortlessly achieves this. I would also like to congratulate you on your lifelong contributions to science, which have had a profound impact on the advancement of knowledge. Thank you for your dedication and inspiration.

[@amyjohoppins1087]

Accolades from a prestigious uni tech from the other side of the world - amazing reach.

[@sb.sb.sb.]

That is great!

[@insulastudios]

Science should make countries closer, I appreciate a lot this message, thank you from Italy

[@Ishanka.]

Oh ah , It means muslim baiya too can understand something 😮

[@sb.sb.sb.]

@@Ishanka....haha apart from Kooran

[@UnchainedEruption]

That is absolutely incredible to have such powers of faculty at age 89, let alone killing it as an all-star Professor. Congrats on a career at MIT spanning 6 decades.

[@user-em1bu1hn9o]

Thank you so much prof. Strang, your impact on millions of students isnt a small thing. Your efforts and hard work in teaching hasn't gone in vain, but have reached many who were in need of that. Thank you so much!

[@andyfox6632]

End of an era! An amazing teacher, a wonderfully helpful person and a legend! Thank you professor Strang! Best wishes to you!!

[@littlebrownrunninghood689]

I'm from India, and I had never heard of this gentleman until I stumbled upon this video. On learning this was the broadcast of the last lecture of a legendary teacher, I listened to the entirety of it with the utmost respect for him. Couldn't help but get emotional towards the end when everyone clapped for him. I wish him a happy and healthy retirement.

[@aayushkrm]

I felt heartbroken and overwhelmed at the same time. What a legend and an unsung hero. Happy retirement Sir Gilbert Strang!

[@mick128]

I took Professor Strang’s course at MIT over 30 years ago. It was a very memorable experience as he spoke so straight forward but yet profound. I still have his text book. Congratulations to him for an amazing 61 years of teaching students.

[@muskansyed2037]

The standing ovations we all want to see ! This is absolutely fantastic age is surely limitless ❤ kudos to his patience his knowledge

[@valverde667]

I remember taking this course midway through my undergraduate career (after the main maths sequences). Holy crap, this dude was such a beast and I loved his lectures. I can't pinpoint why his lectures resonated with me but they did and I am forever grateful.

[@nickyjiang6404]

Although I am not a MIT student, I have been watching Mr.Strang’s lecture for several times on KZbin and I am thankful for all lectures provided by him. Was an honor to watch such enormous lectures. Respect Mr. Strang, from Korea.

[@ivanherreros7773]

Thank you. Seeing prof. Strang videos all I feel is gratitude. Around 2007, as a PhD student, I watched his youtube videos on Linear Algebra and they rescued me. They probably had more impact in shaping my career than anything else that happened then. I even wanted to add these lectures as a reference to my NeuroIPS paper.

[@ultramet]

In a few minutes, I was able to grasp concepts that I couldn’t some 40 years ago. This is a testament to how masterful a teacher Professor Strang is. Thank you for helping an older guy like me “see the beauty” of linear algebra. Best of luck and enjoy your well deserved retirement..

[@feedlivi]

As an university lecturer, I just wanna thank you professor Strang for all the given knowledge.... you are an example of teaching vocation.

[@tharock220]

I took linear algebra at the University of Texas in 2008. My professor knew how awesome professor Strang’s lectures are and told us all to watch them in addition to attending the in class lectures. They were immensely helpful.

[@BenZamzow]

Congratulations and thanks to Professor Strang! He was one of the first to provide lecture videos online, in the pre-KZbin days. An incredible resource. I self-studied linear algebra during the summer of 2002 with his textbook and lectures (via Real Player, if I'm not mistaken), then breezed through the course at my university that fall. Those videos are the main reason why I share my own (microeconomics) lectures & videos on KZbin.

[@alecfox3309]

This guy carried me through my class, and probably saved many others taking Linear Algebra too. Highest respects to them, and may they enjoy their retirement!

[@m.harrisonbaker462]

Thank you MIT and Prof Strang for the lecture series. I re-learned linear algebra from KZbin in my 30s, and this guy was the best lecturer I've ever seen

[@xirbleivs]

For me, the teacher is most noble profession that exists. All teachers have my utmost respect. And this legend, still doing what he loves at an age that most are already retired, deserves all the applause and a wonderfull retirement. May he live long and happily.

[@dchap88]

Professor Strang and the MIT Open Course Ware single handlely gave me the extra content I needed to gain the confidence going into most of my engineering finals. I really appreciate everything Professor Strang and MIT has done for me. Thank you.

[@reubenemmanuel3287]

The best teacher I never had. But thanks to MIT for sharing his linear algebra lectures. He has been a blessing for thousands of his students.

[@birgula.t.2965]

Thank you so much Prof. Strang. We will keep listening and suggesting your lectures.

[@aseemachoudhary5461]

He's the man who made me love linear algebra and gave me a wonderful insight about this beautiful branch of Mathematics. An absolute legend.

[@samirhussain458]

I have been watching this man’s videos ever since the beginning of university, ever since I even discussed linear algebra and I always look back to them as reference! You have always been a life saver Professor Strang, enjoy your retirement!!

[@BibaGuy2010]

Congratulations professor. KZbin recommended your lectures in few last weeks. I was somehow glued to watch entire videos posted even though i studied LA almost 20 years back given the depth on the topic and way of he was explaining the concepts. One would automatically appreciate the care and love he has for the subject. May you have happy and wonderful life in retirement. Hope you still plan to make a video or two or shorts clips once in a while to keep comms open with vast online boundaryless community which KZbin enable. You are nothing short of a real star and role model wish we have more and celebrate.

[@Sagardeep_Das]

Seeing this last lecture from Mr. Strang made me realise just how dedicated and caring the teachers at MIT are. I wish you a happy retirement post teaching life. Thank you sir. Love from India. ❤

[@asterixx6878]

Thank you for everything, dear Professor Strang. It has been a real pleasure following your lessons. Your way of approaching mathematics, with humanity, warmth and understanding of the difficulties that many students have in their mathematics studies, is unparalleled in my opinion. The lessons have been (and still are!) both fun and inspiring, for me and many others around the world. Thank you for everything, dear professor.

[@miknrene]

Professor Strang’s Linear Algebra book was the single best text I used in my entire academic career. My friend was struggling through LA, which was a requirement for her CS degree. I lent her my copy of Strang’s book, and it got her through the class (and on into a successful career as an SDE.). Thank you professor Strang.

[@user-pp8fw9ep3l]

Dear Prof. Gil, I wanted to express my sincere appreciation for the last lecture of your online class on linear algebra at MIT. Your expertise and passion for the subject truly shine through in your teaching. The clarity and depth of your explanations made the complex concepts accessible and engaging. Your dedication to your students' understanding is truly commendable. Thank you for inspiring me and igniting a curiosity for further exploration of linear algebra. Your genuine care for your students and willingness to address questions have left a lasting impression on me. I am grateful for the opportunity to be a part of your class and will carry the knowledge and insights gained from your lecture throughout my academic and professional journey. With gratitude, Fariba ♥♥♥♥♥♥♥♥

[@sonnyobrien]

He wont read this. He doesnt upload the videos. Try send as an email Edit: i am glad i am wrong

[@mitocw]

​@@sonnyobrien The MIT OCW team has been collecting and sending the comments to him.

[@sarithasaritha.t.r147]

@@sonnyobrien get rekt

[@sonnyobrien]

@@mitocw that is an achievement, thank you

[@sonnyobrien]

@@sarithasaritha.t.r147 jokes on you- I made this comment without the confidence yet hoped that it would garner a response directly from MIT allowing the commenter the assurance their message will be received.

[@justalpha3429]

Total respect. Thank you Proff.Gil Strang🙏

[@guitaristxcore]

I have only just started working on an undergraduate degree in Mathematics, however Dr Strangs lectures have been a part of my life for many years now as I have found these videos of him endlessly fascinating. I wish him a wonderful retirement and I hope he can rest easy knowing that his many great contributions will continue to inspire students for many years to come.

[@jelmargerritsen]

Professor Strang, your lectures on Linear Algebra have been invaluable to me - they got me ready for my Physics degree, and later I found myself returning to them when my university's own lectures fell short. You set the standard for math education, one which I will strive to uphold myself. Thank you!

[@chiragraju821]

I had the pleasure of attending your seminar 2 years back, and had a very insightful discussion. Thank you for saving my introductory linear algebra course, which led me to pursue numerical linear algebra and AI research.

[@shocktocker8282]

Fesser- congrats on teaching a complex subject at such a high level over so many years. Thx to MIT for allowing this open course to be broadcast to the public. NOW that I'm retired I enjoy learning from videos like this. Would be GREAT if you could do KZbin videos for public consumption, it would be a contribution to humanity! Good luck & continued success!

[@Idtelos]

Although I did not get to take Dr. Strangs Linear Algebra class, I was taught it by one of his former students (who used Dr. Strangs textbook) who took this class as an undergrad and was one of his advisors. He was one of my advisors and In this, I feel a connection to Dr. Strang. Thank you for all your years of dedication to mathematics and its teachings.

[@nianghuchen]

Without prof. Strang ‘s lectures I could’ve never passed my own linear algebra class ten year ago. A millions thanks❤ and wish you a peaceful and happy retired life!

[@400_billion_suns]

People like this man truly make the world a better place. There’s so much peace and beauty in a life focused on teaching and learning.

[@sydneydahl3428]

Thanks Gil Strang! I got my only A in my math/stat undergrad and it was because of your lectures and the pattern my teacher implemented from your great example and teaching style. I am forever grateful for you exhuberating my love of linear algebra and math!

[@lynx141]

People such as this Professor are such an inspiration. For those unable to be in person in his lectures, videos such as these provide such an invaluable opportunity to learn and to be inspired by such learned minds. For this, thank you MIT.

[@mbraincheck5761]

Got lots of helps from professor Strang when I was preparing for my graduate school. Just feels grateful and appreciate for the works have done. Hope you have a wonderful retire life!

[@imranakhand8750]

It was a pleasant surprise that I came across this video, and more pleasant to listen to this masterclass. Thank you, Professor. Wish you enjoy your retired life happily and in good health.

[@dedekindcuts3589]

Thank you Prof Gilbert Strang for the lectures and textbook on linear algebra. 13 years ago after graduating from high school, Prof Strang's 18.06 MIT OCW series was the first lecture series I watched while waiting to study university math. His lectures emphasised the different ways to think about linear algebra instead of just dry formulas. To this day, I still remember and use his column picture and row picture of matrix multiplication (each column of AB is a linear combination of columns of A) - this is seldom taught elsewhere but it really helped made a lot of reasoning with matrices and linear algebra a lot more intuitive. Used these pictures many times even when learning more advance math and my classmates seldom know about it.

[@JONASACHUOBIMaths]

Any link to any of his books?

[@dedekindcuts3589]

@@JONASACHUOBIMaths I bought his Introduction to Linear Algebra book

[@tirimula]

Thank You, Prof. Gilbert Strang. Your teaching is inspiring for generations to come. We are truly grateful to you Sir!

[@longh]

Thank you Professor Strang for sharing your knowledge throughout the years. Your Linear Algebra course made me fall in love with the subject and I am very grateful!

[@sweatstallion8437]

"If I have seen further than others, it is by standing upon the shoulders of giants."-Issac Newton.... Professor Gilbert Strang you are the giant that students across the world will always stand on. These videos will immortalize your immaculate lectures. Thank you sir for devoting your life to teaching and giving students hope amongst their struggles. The future will be a better place because of humans like you.

[@flipnothling9288]

I am grateful for being able to follow Professor Strang's excellent lectures. A great lecturer and a great man. Congratulations, Professor.

[@jiongwang7645]

I have been benefiting from Professor Strang as a student, and now a teacher. I know a simple "Thank" does not afford to any extend my gratefulness, but still, I think this would be the only simple way online to express a least a bit of it! Thank You!

[@jonahdeykin7521]

I took your linear algebra course on MIT OpenCourseWare, I can confidently say you are one of the best teachers I ever had! Your passion for the subject, and ability to convey mathematical concepts in a digestible manner make you a pleasure to learn from, even if it was only through prerecorded videos. Thank you so much!

[@123XTSK]

His lectures motivated me to learn linear algebra when I was 73years.I then used it to teach my grand daughter at a UC....it was absorbing interesting and motivating....every lecture session.Thanks Prof and my virtual Guru in Lin Algebra.

[@gedavaa1]

Many love from Mongolia. Wish long live Mr. Gil Strang.

[@user-uq5qw1fk3d]

Thanks for everything Gil! Your lectures and book got me through Linear Algebra and kept my interest in mathematics alive over 15 years ago. I still love going back your videos every few years. You've impacted the lives of millions and will live on in our hearts forever, all the best in retirement!

[@steveross4539]

From Prof Strang’s OCW videos and Linear Algebra book I learned there was so much more to it all than just crunching numbers, so thank you. I also say that Pavel’s on line lectures on tensor calculus show that he picked up many of his advisor’s great teaching styles, thank you also. Best wishes.

[@pxdkhoa]

Thank you for everything you have done for students who love Mathematics, especially in Linear Algebra and Calculus, Professor Strang.

[@mathematicia]

Words fail to express the overwhelming emotions that stir within me as I watch Gil Strang's final lecture. At the age of 88, after dedicating a lifetime to the pursuit of knowledge, his retirement brings tears of admiration and gratitude to my eyes. The depth of his wisdom and unwavering passion is a testament to the extraordinary impact he has had on countless lives. Sir, your dedication and love for the subject have touched my heart in ways I can't fully articulate. You have shown me the beauty of a lifelong journey of learning and the profound difference one person can make. As you gracefully step away from the lectern, please know that you have left an indelible mark on the world of mathematics and on the hearts of aspiring learners like myself. Thank you for sharing your remarkable journey with us and inspiring generations to come.

[@vivekjangir629]

Bhai mar var to nahi gya na😂

[@GodofStories]

Well said! One can hope to live as humbly, and work as diligently for a lifetime on a subject as Prof. Strang has.

[@vivekjangir629]

@@mathematicia sorry bro, I thought you ll take it as a joke

[@naserpadar]

I’ve decided to refresh my fragmented knowledge of linear algebra, and judging from the great feedback, I believe it’s the best choice. So, in advance, thank you, Professor Strang!

[@dark_art1]

A professor that will live forever, not only for his unique way of effectively teaching math, but also for his extraordinary ability to make students feel seen, heard and special. Thank you so much professor Strang!

[@sabbirahmed7391]

Professor Gilbert Strang is a great Mathematician and a massive inspiration to the young stars. Wish him all the very best for the rest of his life. Immense love and respect ( Sabbir, Bangladeshi, living in Finland)

[@louisscott471]

18-3 Undergrad. Prof Strang , together with all the professional accomplishments, is a wonderfully kind person. Thank you very much for everything Gil Strang!

[@moosewild4239]

I stumbled on to this video and it was a privilege to watch. Wish Professor Strang the best going forward.

[@SIGINT007]

I love this method of presentation and explanation. When I was in college, the assistants and some professors were so fast, dry and clinical that my brain struggled to stay engaged or comprehend a lot of things. I truly hope this man's students over the years understand the gift they were given by this man.

[@siddhartharoy8978]

I never got a chance to study under him but have read his books which are masterpiece. Deepest respect for him . May God bless him with good health and happiness. Thanks for inspiring many like me.

[@prabathh]

Thank you very much, Prof Strang. Back when I was a student at my uni, I was going through some tough financial times and couldn't make it to the campus for lectures. But guess what? You came to the rescue! Your amazing lectures on OCW helped me not only snag an A+ for linear algebra but also lend a hand to a bunch of other students who were struggling. From the depths of my heart, I send you warm wishes and profound gratitude. Thank you for being such an incredible teacher, and role model. Your legacy will continue to inspire future generations of mathematicians around the world. Happy retirement sir. Lots of love from Sri Lanka.

[@m.y.hamada3784]

It is unfortunate that there aren't more courses taught by Gil on KZbin. I hope you enjoy good health for the rest of your life. Your lectures will never be forgotten.

[@sidmehta1905]

A true legend. An artist who was a bona fide master of his craft. Thanks professor Strang for your generosity in sharing your mind and educating us all! Lots of respect.

[@Pastor_virtual_Robson]

uma despedida muito comovente. felicidades ao professor Gil Strang . Abraços daqui Brasil.

[@a123s1l]

I learnt Linear Algebra from his videos almost 20 years ago and had a chance to briefly meet him at MIT a few years after. What a legend. Thank you Prof. Gilbert Strang for all these years of teaching 🙏🙏

[@lukaruna]

I was one of your many online students. Your fantastic lectures and knowledge changed my life in many ways. If you ever read this, I would like to thank you for everything and wish you all the best. :)

[@Nobodyie]

Increíble persona! Justo ahora empecé a tomar su curso de Álgebra Lineal y me esta gustando. Espero que en alguno años vuelva a este vídeo, mire este comentario y recuerde todo lo que aprendí en sus clases.

[@jjk8417]

Thank you, Professor Strang, for your excellent lectures all these years. You're an absolute master in teaching.

[@ikechukwumichael1383]

Thank you Prof Gil Strang for all I have learned and keep learning from your lectures and for making your contents the first on OCW freely!!! All I have for you is love, great admiration and debt of gratitude Sir.

[@afshinzand220]

knowledge, wisdom, charisma, decency, and many more beautiful things in a wonderful man! What else a student can wish to find in his/her professor? My humble congratulations to professor Strang for his remarkable and outstanding achievements.

[@benwade647]

I spent the last summer holiday watching Mr Gil's 18.06, and it was so great! I have had lectures about linear algebra in my school, but none of them showed any insight at all; they didn't even mentioned vector space which is supposed to be the heart of linear algebra. Mr Gil really helped me a lot

[@shocktocker8282]

AMAZING career, Professor. USA has been blessed to have you teach our children (AND our kid's kid's!). NOW is the time. Look at great athletes who come back after retirement....

[@serdalaslantas]

I have benefited from his linear algebra classes a lot . Thank you Gil for your dedication. You are good example to the new generations .

[@msg2clash]

Wonderful teaching style, I'm returning to education much later in life after leaving it young, Gil's approach makes advanced math concepts accessible and have watched many of his lectures and other MIT Lectures from Ireland, it's a truly wonderful resource to experience these classes and get fired up when something clicks Thank You, Professor Strang, have a very happy retirement.

[@mehranpiran3525]

Dear Professor Strang, your linear algebra courses is a real treasure, a great learning opportunity for all the researchers in different interdisciplinary fields. May your retirement be filled with joy and fulfillment ❤

[@himanshutiwari3828]

In the realm of mathematics, a luminary shines, Gilbert Strang, a soul of boundless lines. With elegant grace, his words do flow, Unraveling secrets that numbers bestow. In lecture halls, his voice resounds, A symphony of wisdom that astounds. He weaves matrices and vectors, so profound, Creating symmetries where solutions are found. Through Linear Algebra's intricate dance, He unveils the beauty of matrices' expanse. Transformations and spaces, he unveils their might, Guiding seekers toward mathematical light. A teacher, mentor, with compassion so true, Gilbert Strang, a guiding star, we pursue. His passion for learning, forever ablaze, Igniting minds, illuminating endless pathways. His legacy inscribed in minds he's touched, A catalyst for minds that were once clutched. Gilbert Strang, your impact shall endure, A maestro of numbers, forever pure!

[@IQ-303]

Thanks, ChatGPT!

[@shahrukh877]

@@IQ-303 You're welcome, Bard!

[@yoyowang9909]

dr strang is such a previous soul with a genuine, warm, and inviting energy. his lectures make me love math. you are amazing, dr. strang !!! thank you for all your invaluable contributions.

[@m0zzar353]

previous soul moment

[@yoyowang9909]

so previous

[@andrewnguyen777]

Professor Gilbert Strang’s lectures truly made me more interested beyond what I was learning in the classroom. The way he conveyed, the way he encouraged, the way he showed and told a story with math or showing how to tell a “a story” with math, all of it and more kept me engaged or explore even if just a little beyond discussions in class. These VODs re-flourished my appreciation and excitement for math after having it snuffed off by many monotonous professors or instructors who’ve made me eventually take on “just taking this for the credit requirements but idk why else” mindset before I realized it-and this is me coming from the MIT of the South, tongue-in-cheek. Thank you tremendously MIT OCW and Gil Strang for all you do and inspire to do for the betterment of the world, generating, disseminating, and preserving knowledge. I am joyed that Professor Gil has seen the generous messages and testimonies of his impact and legacy. I wish a blessed well-off retirement to you sir Strang!

[@marklamias7763]

Congratulation on your retirement Professor Strang! We are forever indebted to you for your carefully crafted lectures and education you have brought to so many. I must tell you that I took my first two linear algebra courses from Richard Canary at the University of Michigan and several years after graduating, I needed to refresh myself on some concepts from the courses I took. Your material was the only really accessible material I could find and was perfect in every way. Succinct, yet sufficiently detailed for a post-graduate student needing to refresh his linear algebra skills prior to running some advanced simulation models with heavy use of matrices. Thanks again for all you've done. I hope you enjoy your retire and know the impact you've had on countless people and the applications, inventions they've subseqently brought forward that youv'e had a hand in, in some sense!

[@OswaldChisala]

I love this man. He gave me the confidence to do mathematics again after I dropped out of college. He deserves all the amazing energy he's received now and throughout the years. Stay blessed, Professor Strang!

[@user-re1qy6kd6p]

⏱Timestamps for this video! 0:00 - Introduction to the class event 10:05 - Alan Edelman's speech about Gilbert Strang 12:57 - Gilbert Strang's introduction 15:42 - Solving linear equations 30:42 - Visualization of four-dimensional space 31:37 - Nonzero Solutions 32:16 - Finding Solutions 34:19 - Elimination Process 41:05 - Introduction to Equations 42:26 - Finding Solutions 44:29 - Solution 1 47:42 - Rank of the Matrix 51:39 - In appreciation of Gilbert Strang 52:08 - Congratulations on retirement 52:38 - Personal experiences with Strang 55:01 - Life lessons learned from Strang 1:01:08 - Gil Strang's impact on math education 1:01:44 - Gil Strang's teaching style 1:02:20 - Gil Strang's legacy 1:03:23 - Congratulations to Gil Strang 🧙‍♂✨ Generated with Houdini Chrome extension.

[@ashirwadgarg174]

I can't believe this is his last lecture. 🥲Sir you are G.O.A.T of linear algebra. Thank you sir. Love from India. ❤

[@wasa1997]

I've never met Gil Strang, only know him through his KZbin lectures, but I feel like I know him (and all the other MIT professors who have made their instruction available through MIT Open Courseware). His linear algebra lecture(s) have been a tremendous discovery for me--a 50 year old English major. I had a few tears in my eyes watching this. Congratulations to Prof. Strang, and thanks for all you have done for students at MIT and throughout the world.

[@ue4152]

Ahh, I passed my Math201 Linear Algebra course thanks to dear Prof. Gilbert Strang back in time. As a robotics engineer now, I still use the knowledge I learned from him. Truly a teacher. I wish him great success and happiness for whatever lies for him next.