Diagonalization

[@Dan-jq7eq]

This man really just explained 2 weeks worth of content in 8 minutes, what am I paying all this tuition for 🙃

[@weichang8634]

the degree dummy

[@irishuang8726]

no fr

[@inquisitionagent9052]

The piece of paper

[@abdirahmanalimohamed5925]

@@inquisitionagent9052 Mmm mm

[@chathurikadilhani1951]

Really 🔥how effective this is 💯

[@greendino9918]

Prof Dave, thank you so so much! You literally helped me survive my first year of engineering (calculus, chemistry, and physics) and now I'm back for my second year! Your visuals are so amazing and they make everything super easy to understand!! I just want to let you know that you're doing amazing work and we stem students appreciate you so much!

[@noellelavenza]

My professor hasn't lectured all semester and just pointed us at the textbook, and this was the last topic I didn't fully get on my own before our exam today. You're a lifesaver.

[@cameraman4401]

Lemme hit🤤

[@azadprasad856]

Congratulations professor Dave for becoming a father!

[@MedinipuriTuka036]

Did he really ?😮

[@ddodd69]

late...

[@Prof.afterMATH]

This is always a hard topic to teach. This is straight forward and clear. Great video!

[@nishantbanjade920]

Sir I'm from Nepal ,because of your tutorials I'm able to grab schlorship of $35K . thanks sir

[@shreejanshrestha1931]

That's amazing brother. Kun thau ma k ko payeko ho? Anyway congratulation dhilai vayeni hai. Jay Nepal

[@habondoemmanuel7558]

Professor you're really supercalifragilisticexpialidocious

[@fizzy4149]

I have a PhD in math but professor Dave is so much more well rounded than myself. He's doing matrix algebra here and I'm using his videos to get the gist of population evolution and abiogenesis.

[@mikuculus3720]

Yea idk how he knows all the physics and math at a level he knows

[@youtubecubedude8940]

Prof Dave is great at teaching, but it’s really the editing that makes these videos so easy to understand.

[@khayalethumakosi6678]

daaaain!!!! you are also a monster!!!

[@ephemeronchimera]

Prof Dave: I am currently doing self-study of every math course required for an undergraduate math program and I was having a hell of a time understanding fully how to perform diagonalization! I have read countless textbooks' sections on diagonalization and watched several other videos. I took thorough notes from your mini lecture, followed along with you on the example and am stoked to say I was able to go through the example problem at the end and got everything right. ALSO...nowhere else has anyone mentioned to ALWAYS choose x2=1. That tiny detail helped make everything else click and I agree with you that the process of diagonalization is in fact easy, albeit time-consuming. I cannot thank you enough for this! The way you go through and show every single detail is a TREMENDOUS help! I really appreciate you!

[@yash1152]

7:41 "so, lets check comprehension" wowww, never seen that part in any other video. awesome, thanks a lot for including that :)

T - 7:17:00 until the exam, thank you! Learned what was chaotically taught in two weeks in under two hours with notes taken and examples calculated by watching two of your videos. The 222 (*3 :])

[@conzopontsho3253]

I am from South Africa, because of you i have managed to get My Degree. Thank you so much

[@jevcampbell2301]

THANK YOOUUU SOO MUCH ... HOLY it's people like you why I'm able to go back to school and have hope.. keep doing what you're doing you're helping the mental health of people everywhere... I was so depressed... cause I can't get this and my finals consist mostly of this ... this really helps.. thanks so much.

[@nolapickering1917]

You're such an incredible teacher! Textbooks are so esoteric where your videos are so accessible :) thank you for your work

[@trainwithyv1011]

4:13 , why did you choose x2 = 1, why not x1 = 1? If we take x1 = 1 will our answer be the same ?

[@deuslapis5247]

I'm currently binging as many linear algebra videos as i can for an upcoming final and i gotta say, yours is really really good.

[@mohsen865]

thank you professor. every teacher must see you videos first to be qualified for teaching

[@Creekilljoy]

This definitely simplified everything that was taught to me in my class lecture. Everything is super clear now. Thank you so much!

[@TenaciousDanR]

Great video! This helped me so much. I know this is a little late but I just wanted to point out that instead of calculating X inverse to check your answer at the end, you can simply check to see if AX = XD . This is much easier if you are asked a similar question that uses nxn matrices where n > 2 as the computing the inverse becomes more annoying as n increases.

[@chimphead73]

XD

[@infernon]

@@chimphead73 LOL!!!!!!!!!!!

[@joserobertopacheco298]

Congratulations for you job, Professor Davis. You make mathematics easy to understand. I wish you were my teacher.

[@wavvy94]

How is it that I sat through two lectures on diagonalisation and it hardly made sense, yet after watching this video the entire concept could NOT be any simpler?? Actual lifesaver, I'm defs getting 100% on my linear algebra quiz tomorrow

[@khadijehRab]

كل مرة بحضر فيديوهات للبروفيسور بطلع فاهمه، طريقته بالشرح مثالية ، ممتنه جدا

[@Anna-qp1fi]

Professor Dave will go down in history as one of the greatest legends of all time.

[@timothyli2820]

Hi Professor Dave! You helped me sooo much before my test! U saved me and my classmates!

[@Jerry_TheLittleOne]

This is indeed a pure gem! Thank you for posting it 👏

[@enes4642]

You saved me a lot of time Dave. Thanks for the incredible video series.

[@komare5344]

Quick thank you to Professor Dave and others like him for the fact that i can just type in a subject i want to learn about and i easily find a few minute video about it that is easy to understand :)

[@YUMYUMINMYTUMTUM]

Taught the entire concept so easily. WAY BETTER THAN MY T100 UNI LECTURER

[@Brantendo64]

@4:48 Why can we just choose x2 = 1? Don't you get x2 by subtracting 5x and dividing 4 giving you x2= 5x/4 ?

[@sheerazkhan1730]

Did you get your answer?

[@tofubtofub]

Universities around the world NEED professor like you.

[@MuhammadIbrahim-nx9fg]

loved the video. thank you for saving my academics.

[@Iffat-id9js]

Thanks Mr Dave for making the topic so easy😊

[@petrineys5184]

This was honestly so good. Thank you.

[@rolandoblest610]

Your videos are excellen. In my native language: Sus vídeos son excelentes. Thanks a lot

[@Abhraneil_Bhattacharya]

sus

[@lahirujeewantha5208]

Thanm you so much sir.. This is another vedio I understood whole concept from you.. you are such a prolific teacher.. Wooh!

[@noorulain7111]

5:19 How will we know that in which sequence we put the eigen vectors ,is there any rule of it or we can just randomly put any eigen vector in first coloum or second column.?

[@fernanmontevista204]

I reading my linear algebra book but i cant comprehend .Looking for several videos but im still confuse halfway.. This is the video that enable me to understand it clearly. Thanks Dr Dave.

[@mistuhfunny]

6:52 why did he multiply DX^-1 first instead of XD?

[@IshikaSharma-y9x]

It doesn't matter you will get the same answer...

[@nozawatakahiro7730]

Thank you, Prof Dave. This video made me clear in this topic otherwise some of text books written in Japanese are so hard to understand for newbie.

[@alann3963]

i m from kerala , india Well class Thank you sir, ☺️

[@adhiyanthaprabhujeyashanka2091]

I'm from tamilnadu 😂

[@limitedquantitysufiyyahexp4905]

I don't understand anything 🤯😭😭

[@quaminafetchout234]

Please why do you normally choose X2=1 I don’t get that part

[@shreejanshrestha1931]

P.S. in 6:45 ( A= X-1 D X ) is known as eigenvalue decomposition

[@Ggk5392]

great explanation. Thank you so much

[@yashvats9703]

Professor Dave rocks🤘🤘

[@AlexPredict]

Nice explain sir i love it😍❤

[@samara9221]

My brain hurts

[@kimdull]

best explanation i ever seen entire KZbin videos !!!! I have question does D has to be in order of 1 0 0 2 or it doesn't matter if it was 0 2 1 0 ?

[@Entervation]

The values in D are the eigenvalues, order them from lowest on the top left to highest on the bottom right, following the diagonal :) (As shown from 7:58 and onwards)

[@jota1858]

@@Entervation thnx a lot

[@thebestworst8002]

Where was this series the beginning of the semester? I now have to cram so much information the days before my final.

[@damianomartucci9814]

Thank you! I can't understand why professors complicate things so much!

[@faraday3833]

thanks! but i keep finding X inverse's last row as [ -1,-1 ] instead of [ 5,5 ] at 6:26. I am using the method of reducing the A with its Identity matrix. I also used some online matrix inverse calculators, also they are giving me my result instead of this video's. Are they just mean same thing? Or the video is not correct?

[@mouhametcheikhdiop5296]

Thank you so much , this is the best i’ve found !

[@shubhreetbhullar4845]

When I multiplied X^-1DX, the result was not A it was A with the -1 and 2 switched places. Did I do something wrong or is this how it is supposed to be?

[@hana29971]

It was X(D)X^-1 as matrix multiplication is not commutative

[@willynannbalenia564]

You are so good at what you do. i hope I become like you in terms of teaching! So cool!

[@resey1999]

Sir, you saved my life

[@زينباحمدعبدالله-ص1ي]

Thank you so much professor for your explanation. Good luck

[@tomatrix7525]

Very helpful. Just a tip, I find there is a bit too much talking in reference to general examples and I tend to get confused and loss. Jump to numerical examples quicker in my opinion could work out better in terms of comprehenion, IMO ofc...

[@leoshi1418]

How did you just make me understand this so easily :D

[@chathurikadilhani1951]

Thank you so much 🔥❤️perfect explanation 💯

[@sayanjitb]

Thanks prof. Dave for your amazing comprehensive but precise talk on linear algebra. In this particular video why are we supposed to take X2 equal to 1 for every time as you were taking? Is this a free variable that allows us to assign any value to it or just for ease calculation as well! Thanks in advance.

[@tinyasira6132]

did u get this ans? i wanna know too

[@joaocosta3506]

@@tinyasira6132 its because it is a free variable, if you reduce to echelon form you'll see that the only pivot will be x1, therefore the x2 will be a free variable.

[@kanishka.s.jaeronauticalen8053]

Your teachings are so awesome sir thankyou

[@ruubelynd9902]

thanks for the learnings prof dave. But i would like to see the 3x3 matrix happen when you have both 2 rows are all zeroes.. Thank you. I hope you will notice this.

[@allbeautyariethang8594]

at 4:51 you said choosing x2 to = 1 why did you choose 1 or just assume a random number. could you explain please

[@maartenkeus8627]

it's looking like you just always normalize for x2 = 1, makes sense cause that is the most convenient

[@haroldvillacorte2092]

Great explanation! Thanks!

[@Crick_edt]

Great explanation sir

[@georgiasonter1842]

Hi Professor Dave, Thanks for the great linear algebra videos. At around 7:00, why did you multiply D by X inverse first? Instead of multiplying matrix X by matrix D first? I didn't think that matrix multiplication was commutative?

[@ProfessorDaveExplains]

not being commutative simply means that we can't reverse the order in which we list the matrices, but we can simplify in any order we want, if you do the other multiplication first you should get the same answer

[@azhua123]

where do the -4's go at 3:57?

[@I.M.UMmU.]

Clearly he told ,÷-4

[@ethanjiang7070]

very clear explanation!

[@aggelosladas1326]

in both cases (4:56) you said choosing x2 is equal to 1? you just assume x2 is equal to 1 and i don't understand how you get x2 to be 1.

[@hana29971]

You can assume any value for x2 or x1 ,it'll all be a scaler multiple of when x2 or x1 =1

[@karenkamimasumaili137]

How do you know which eigen vector to use first and second to make up the eigen vector matrix?

[@ajeetchella4747]

excellent explanation

[@sayeedahmed3609]

I can see some light for my engineering degree because of you. Could add one video for change of basis in linear transformation. I feel abstracts with my university resources.

[@ProfessorDaveExplains]

I did that! Check the linear algebra playlist.

[@kaushikdr]

Can you explain what XDX-1 means? I understand XD is a matrix of the scaled eigenvectors after the transformation A and X-1 is the inverse of X. However, I don't know what it means for a matrix to be the inverse of the eigenvectors.

[@louiswouters71]

If you want to fully understand it, I suggest you watch 3blue1brown's videos about linear algebra, but here is the short version. The matrix A is a matrix that transforms space, everything gets shifted except for the eigenvectors, they just get longer. So what we can do is first map the eigenvectors to our unit vectors (X^-1), then scale those vectors (D), then map them back to the eigenvectors (X). Since these are all linear transformations, this is not only true for the eigenvectors, but also for all other vectors in the 2D plane. So XDX^-1 = A.

[@yokubjonabralov6294]

Wow thank you, I finally understood this stuff

[@arisnikou04]

Professor Dave casually saving everyone's ass again this year

[@babajan5370]

amazing I understand BST ❤ thnks

[@cedricsipakam2601]

I love your content so much !

[@yomihost2732]

It really helps me! Thanks a lot!

[@samaawagih7272]

Thank You!🥰🥰

[@Iffat-id9js]

Is there only two videos relating to the eigen topic?

[@35someguy79]

Linear Algebra - Ego = Professor Dave. You are fantastic. Thank you.

[@hatelovebowel4571]

professor dave, how do you know how to put the 1 and 2 in that order in the diagonal matrix?

[@mattsamfab]

wish he answered this

[@XBJASHITHABATULA]

great explaination

[@shardx191]

what do you mean by unique eigenvalues? I don't understand the conditions for the possibility of diagonalization and wish u provided some examples on it aswell.

[@ProfessorDaveExplains]

Check the earlier tutorial on eigenvalues and eigenvectors.

[@rayadelavega8766]

I love you you're a lifesaver!

[@lisajose9219]

Really talented.keep it up.

[@abhivaryakumar3107]

Thank you professor dave Just thank you You are saving me from failing my math class

[@Kloziee]

At the last one I had the same eigenvalues 4 and 5 but I turned them around in matrix D. Is that wrong is doesnt it matter?

[@srinityapadma5125]

Thank you so much Sir.../\ It is so easy to understand your explanations Sir...

[@qefeng2254]

Hi, do you have a video to explain why this works?

[@MuhammadYasir-y2t]

Appreciated God bless u man

[@sohailaihab1533]

God Bless you Sir

[@immortalspiritualbeing7037]

very clear, thank you

[@yusraq6329]

what is the rule behind choosing x2 to equal 1?

[@alenasahoo3107]

you're amazing thank you so much

[@esqucimenaosei5482]

amazing how an 8 minute video explains everything that an university teacher cant in 2 hours

[@pietlemao8491]

Thanks so much prof

[@michaelharris1884]

what do you do if thie L is only equal to one number like for example "L^2+4L+4" will be only equal to -2. Would I use the same one to make two of the same thing? like I get [3,1] for one of my eigen vectors, then would I just write the same thing for my 2nd eigen vector [3,1]

[@CheeHinChoa]

for A = [6 , -1, 2, 3], I got D = [5, 0, 0, 4]. X = [1, 0.5, 1, 1] instead of D = [4, 0, 0, 5] X= [0.5, 1, 1, 1]. Does choosing eigenvalues matter? lile lamda1 = 4, lamda2 = 5, instead of lamda1 = 5, lamda2 = 4

[@zalko_]

it has no impact as long as the order of your eigenvalues and eigenvectors correspond which you seem to have done right

[@ranjithabc9004]

Please make a video on exponential matrix

[@muthiahpillaipalanichamy3939]

Great Professor