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!

[@azadprasad856]

Congratulations professor Dave for becoming a father!

[@noellelavenza494]

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.

[@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

[@Prof.afterMATH]

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

[@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!

[@nolapickering1917]

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

[@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!!!!!!!!!!!

[@conzopontsho3253]

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

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 :])

[@khadijehRab]

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

[@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.

[@kevingarza6862]

This definitely simplified everything that was taught to me in my class lecture. Everything is super clear now. 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.

[@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

[@timothyli2820]

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

[@mohsen865]

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

[@Anna-qp1fi]

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

[@tofubtofub]

Universities around the world NEED professor like you.

[@joserobertopacheco298]

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

[@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

[@Jerry_TheLittleOne]

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

[@Iffat-id9js]

Thanks Mr Dave for making the topic so easy😊

[@enes4642]

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

[@thebestworst8002]

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

[@petrineys5184]

This was honestly so good. Thank you.

[@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.

[@yash1152]

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

[@MuhammadIbrahim-nx9fg]

loved the video. thank you for saving my academics.

[@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.

[@lahirujeewantha5208]

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

[@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 :)

[@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.

[@rolandoblest610]

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

[@Abhraneil_Bhattacharya]

sus

[@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...

[@Ggk5392]

great explanation. Thank you so much

[@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 ?

[@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 🤯😭😭

[@shreejanshrestha1931]

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

[@resey1999]

Sir, you saved my life

[@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.

[@XBJASHITHABATULA]

great explaination

[@arisnikou04]

Professor Dave casually saving everyone's ass again this year

[@AlexPredict]

Nice explain sir i love it😍❤

[@souviksen3362]

Great explanation sir

[@damianomartucci9814]

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

[@haroldvillacorte2092]

Great explanation! Thanks!

[@pietlemao8491]

Thanks so much prof

[@samaawagih7272]

Thank You!🥰🥰

[@ethanjiang7070]

very clear explanation!

[@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

[@ajeetchella4747]

excellent explanation

[@trainwithyv1011]

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

[@mouhametcheikhdiop5296]

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

[@yashvats9703]

Professor Dave rocks🤘🤘

[@babajan5370]

amazing I understand BST ❤ thnks

[@kanishka.s.jaeronauticalen8053]

Your teachings are so awesome sir thankyou

[@زينباحمدعبدالله-ص1ي]

Thank you so much professor for your explanation. Good luck

[@willynannbalenia564]

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

[@immortalspiritualbeing7037]

very clear, thank you

[@alkhaled4976]

Perfect

[@quaminafetchout234]

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

[@babajan5370]

excellent sir

[@danielwahl9937]

Thanks

[@yusraq6329]

what is the rule behind choosing x2 to equal 1?

[@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

[@leoshi1418]

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

[@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.

[@Myron19]

Super video!

[@35someguy79]

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

[@abhivaryakumar3107]

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

[@sohailaihab1533]

God Bless you Sir

[@lisajose9219]

Really talented.keep it up.

[@yomihost2732]

It really helps me! Thanks a lot!

[@chathurikadilhani1951]

Thank you so much 🔥❤️perfect explanation 💯

[@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

[@yokubjonabralov6294]

Wow thank you, I finally understood this stuff

[@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.?

[@muthiahpillaipalanichamy3939]

Great Professor

[@williambyamukama2251]

Thank u professor

[@gooseberry_disliker]

thank you so much!!!!

[@nourhh_]

thank you so much!

[@sandippaul468]

Can't thank you enough.

[@cedricsipakam2601]

I love your content so much !

[@STKeTcH]

THANK YOU

[@ranjithabc9004]

Please make a video on exponential matrix

[@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

[@caglabot]

thanks prof dave, although i'm lost as to how and why i need to know this for my industrial engineering diploma.

[@Mathskylive]

Diagonal matrices have many applications in computing.

[@sumayyakamal8857]

prof David, thanks a million for your great vids! so how would a non-diagnolizable matrix look like, how to know that? I mean from the first step we won't be able to get eigen values?

[@romanpashkovsky3480]

hey, I suppose your question had been already answered by this time, but just in case, an n x n matrix is diagonalizable if and only if it has at least n linearly independent eigenvectors. If it doesn't, then you know it's not diagonalizable.

[@hugeturnip3520]

thnak you so much

[@srinityapadma5125]

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

[@cindycindy5980]

For the comprehension question I got to: a = 4, eigenvector = 1, 1 b = 5, eigenvector = 1, 0.5 how come the first column of X is 1/2 1 instead of 1 1?

[@nerd2544]

3 months late but order of columns determines your diagonal matrix. if 1/2 1 was the SECOND column of X, instead of D = [ 4 0 5 0 ], you would get D = [5 0 4 0] please see 2:05 of the video

[@karenkamimasumaili137]

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

[@destaabayneh7416]

thanks sir