Diagonalization

Рет қаралды 489,444

Күн бұрын

Now that we know about eigenvalues and eigenvectors, we are ready to learn about diagonalization. This involves writing a matrix as a product of other matrices, one of which is a diagonal matrix, with values only along the main diagonal. This has many applications in computation, so let's take a look!
Script by Howard Whittle
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@Dan-jq7eq Жыл бұрын

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

@weichang8634 Жыл бұрын

the degree dummy

@irishuang8726 Жыл бұрын

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@inquisitionagent9052 Жыл бұрын

The piece of paper

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@chathurikadilhani1951 Жыл бұрын

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@azadprasad856 5 жыл бұрын

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@nishantbanjade920 5 жыл бұрын

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@shreejanshrestha1931 3 жыл бұрын

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@habondoemmanuel7558 Жыл бұрын

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@greendino9918 3 жыл бұрын

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!

@noellelavenza494 3 жыл бұрын

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.

@Prof.afterMATH 4 жыл бұрын

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

@fizzy4149 Жыл бұрын

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 3 ай бұрын

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

@nolapickering1917 Жыл бұрын

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

@kevingarza6862 3 жыл бұрын

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

@ephemeronchimera Ай бұрын

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!

@deuslapis5247 2 жыл бұрын

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.

@youtubecubedude8940 Жыл бұрын

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

@khayalethumakosi6678 6 ай бұрын

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

@joserobertopacheco298 4 жыл бұрын

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

3 жыл бұрын

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 :])

@enes4642 6 ай бұрын

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

@komare5344 Жыл бұрын

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 :)

@conzopontsho3253 3 жыл бұрын

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

@Anna-qp1fi 2 жыл бұрын

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

@timothyli2820 4 жыл бұрын

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

@jevcampbell2301 3 жыл бұрын

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.

@petrineys5184 Жыл бұрын

This was honestly so good. Thank you.

@Jerry_TheLittleOne 4 ай бұрын

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

@nozawatakahiro7730 2 жыл бұрын

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.

@yash1152 2 жыл бұрын

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

@MuhammadIbrahim-nx9fg 3 жыл бұрын

loved the video. thank you for saving my academics.

@tofubtofub 3 жыл бұрын

Universities around the world NEED professor like you.

@willynannbalenia564 Жыл бұрын

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

@fernanmontevista204 2 жыл бұрын

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.

@wavvy94 2 жыл бұрын

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

@mohsen865 3 ай бұрын

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

@mouhametcheikhdiop5296 3 жыл бұрын

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

@Ggk5392 4 жыл бұрын

great explanation. Thank you so much

@Iffat-id9js 5 ай бұрын

Thanks Mr Dave for making the topic so easy😊

@user-ye8pt5fg1c 2 жыл бұрын

Thank you so much professor for your explanation. Good luck

@yomihost2732 3 жыл бұрын

It really helps me! Thanks a lot!

@lahirujeewantha5208 6 ай бұрын

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

@haroldvillacorte2092 Жыл бұрын

Great explanation! Thanks!

@damianomartucci9814 3 жыл бұрын

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

@TenaciousDanR 2 жыл бұрын

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 2 жыл бұрын

@infernon Жыл бұрын

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

@kanishka.s.jaeronauticalen8053 3 жыл бұрын

Your teachings are so awesome sir thankyou

@ethanjiang7070 3 жыл бұрын

very clear explanation!

@yokubjonabralov6294 3 жыл бұрын

Wow thank you, I finally understood this stuff

@leoshi1418 2 жыл бұрын

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

@rolandoblest610 3 жыл бұрын

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

@Abhraneil_Bhattacharya 2 жыл бұрын

sus

@thebestworst8002 Ай бұрын

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

@srinityapadma5125 3 жыл бұрын

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

@chathurikadilhani1951 Жыл бұрын

Thank you so much 🔥❤️perfect explanation 💯

@cedricsipakam2601 Жыл бұрын

I love your content so much !

@user-saint Жыл бұрын

Great explanation

@ajeetchella4747 3 жыл бұрын

excellent explanation

@immortalspiritualbeing7037 2 жыл бұрын

very clear, thank you

@abhivaryakumar3107 Жыл бұрын

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

@tomatrix7525 3 жыл бұрын

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...

@souviksen3362 Жыл бұрын

Great explanation sir

@lisajose9219 2 жыл бұрын

Really talented.keep it up.

@mohamedabdosalam7093 Жыл бұрын

thanks alot, you are the best

@yashvats9703 3 жыл бұрын

Professor Dave rocks🤘🤘

@AlexPredict Жыл бұрын

Nice explain sir i love it😍❤

@shreejanshrestha1931 3 жыл бұрын

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

@Brantendo64 3 жыл бұрын

@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 ?

@caglabot 3 жыл бұрын

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

@ruubelynd9902 11 ай бұрын

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.

@alenasahoo3107 Жыл бұрын

you're amazing thank you so much

@sandippaul468 3 жыл бұрын

Can't thank you enough.

@muthiahpillaipalanichamy3939 3 жыл бұрын

Great Professor

@XBJASHITHABATULA Ай бұрын

great explaination

@pietlemao8491 9 ай бұрын

Thanks so much prof

@alkhaled4976 4 жыл бұрын

Perfect

@resey1999 27 күн бұрын

Sir, you saved my life

@samaawagih7272 Жыл бұрын

Thank You!🥰🥰

@nourhh_ 3 жыл бұрын

thank you so much!

@sohailaihab1533 4 жыл бұрын

God Bless you Sir

@alann3963 3 жыл бұрын

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

@adhiyanthaprabhujeyashanka2091 3 жыл бұрын

I'm from tamilnadu 😂

@limitedquantitysufiyyahexp4905 3 жыл бұрын

I don't understand anything 🤯😭😭

@trainwithyv1011 7 ай бұрын

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

@arisnikou04 10 ай бұрын

Professor Dave casually saving everyone's ass again this year

@Myron19 2 ай бұрын

Super video!

@noorulain7111 2 жыл бұрын

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.?

@esqucimenaosei5482 2 жыл бұрын

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

@sayanjitb 4 жыл бұрын

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 2 жыл бұрын

did u get this ans? i wanna know too

@joaocosta3506 2 жыл бұрын

@@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.

@STKeTcH 3 жыл бұрын

THANK YOU

@babajan5370 Жыл бұрын

excellent sir

@babajan5370 Жыл бұрын

amazing I understand BST ❤ thnks

@kimdull 4 жыл бұрын

best explanation i ever seen entire KZfaq 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 4 жыл бұрын

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 3 жыл бұрын

@@Entervation thnx a lot

@sayeedahmed3609 2 жыл бұрын

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 2 жыл бұрын

I did that! Check the linear algebra playlist.

@jatirijhatjhat Жыл бұрын

that was so clear!!!!!! thank you!!! Really appreciate this.

@karenkamimasumaili137 7 ай бұрын

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

@ranjithabc9004 2 жыл бұрын

Please make a video on exponential matrix

@shubhreetbhullar4845 Жыл бұрын

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?

@luminousvalentine8011 Жыл бұрын

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

@danielwahl9937 2 жыл бұрын

Thanks

@hugeturnip3520 2 жыл бұрын

thnak you so much

@qefeng2254 8 ай бұрын

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

@williambyamukama2251 7 ай бұрын

Thank u professor

@tymofei8586 2 жыл бұрын

How pure complex eigenvalues of rotation matrix cause rotation by actual elongation with factor lets say 'i' ? Should i think complex plain as 4 dimensional to grasp it intuitively because it doesnt make sense at all like how multiplying complex eigenvector by unit 'i' will scale it in a way so its projection on real plane will be seen as rotation of components of real vectors?

@kingkoller1503 Ай бұрын

Damn, your videos are so great....

@35someguy79 6 ай бұрын

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

@kaushikdr 3 жыл бұрын

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 2 жыл бұрын

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.

@georgiasonter1842 4 жыл бұрын

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 4 жыл бұрын

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