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!
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.
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.
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!
You're such an incredible teacher! Textbooks are so esoteric where your videos are so accessible :) thank you for your work
3 роки тому+5
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 :])
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.
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.
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
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 :)
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.
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)
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?
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.
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...
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 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.
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.
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.?
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]
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.
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.
![Diagonalizing 3x3 Matrix - Full Process [Passing Linear Algebra]](http://i.ytimg.com/vi/0kA_VqHSpGg/mqdefault.jpg)
This man really just explained 2 weeks worth of content in 8 minutes, what am I paying all this tuition for 🙃
the degree dummy
no fr
The piece of paper
@@inquisitionagent9052
Mmm mm
Really 🔥how effective this is 💯
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!
Congratulations professor Dave for becoming a father!
Sir I'm from Nepal ,because of your tutorials I'm able to grab schlorship of $35K . thanks sir
That's amazing brother. Kun thau ma k ko payeko ho? Anyway congratulation dhilai vayeni hai. Jay Nepal
Professor you're really supercalifragilisticexpialidocious
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.
This is always a hard topic to teach. This is straight forward and clear. Great video!
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.
Yea idk how he knows all the physics and math at a level he knows
Prof Dave is great at teaching, but it’s really the editing that makes these videos so easy to understand.
daaaain!!!! you are also a monster!!!
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!
You're such an incredible teacher! Textbooks are so esoteric where your videos are so accessible :) thank you for your work
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 :])
I am from South Africa, because of you i have managed to get My Degree. Thank you so much
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.
كل مرة بحضر فيديوهات للبروفيسور بطلع فاهمه، طريقته بالشرح مثالية
، ممتنه جدا
This definitely simplified everything that was taught to me in my class lecture. Everything is super clear now. Thank you so much!
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.
Professor Dave will go down in history as one of the greatest legends of all time.
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.
XD
@@chimphead73 LOL!!!!!!!!!!!
Hi Professor Dave! You helped me sooo much before my test! U saved me and my classmates!
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
thank you professor.
every teacher must see you videos first to be qualified for teaching
Congratulations for you job, Professor Davis. You make mathematics easy to understand. I wish you were my teacher.
Universities around the world NEED professor like you.
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 :)
7:41 "so, lets check comprehension" wowww, never seen that part in any other video. awesome, thanks a lot for including that :)
Where was this series the beginning of the semester? I now have to cram so much information the days before my final.
loved the video. thank you for saving my academics.
This is indeed a pure gem! Thank you for posting it 👏
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.
Your videos are excellen. In my native language: Sus vídeos son excelentes. Thanks a lot
sus
4:13 , why did you choose x2 = 1, why not x1 = 1?
If we take x1 = 1 will our answer be the same ?
This was honestly so good. Thank you.
You saved me a lot of time Dave. Thanks for the incredible video series.
i m from kerala , india
Well class
Thank you sir,
☺️
I'm from tamilnadu 😂
I don't understand anything 🤯😭😭
Professor Dave casually saving everyone's ass again this year
Thanks Mr Dave for making the topic so easy😊
Thanm you so much sir.. This is another vedio I understood whole concept from you.. you are such a prolific teacher.. Wooh!
Sir, you saved my life
great explanation. Thank you so much
@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 ?
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.
Thank you! I can't understand why professors complicate things so much!
best explanation i ever seen entire UA-cam 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 ?
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)
@@Entervation thnx a lot
P.S. in 6:45 ( A= X-1 D X ) is known as eigenvalue decomposition
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?
It was X(D)X^-1 as matrix multiplication is not commutative
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.
great explaination
Please why do you normally choose X2=1
I don’t get that part
amazing how an 8 minute video explains everything that an university teacher cant in 2 hours
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...
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.
did u get this ans? i wanna know too
@@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.
Thank you professor dave
Just thank you
You are saving me from failing my math class
Thank you so much , this is the best i’ve found !
amazing I understand BST ❤ thnks
You are so good at what you do. i hope I become like you in terms of teaching! So cool!
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.
I did that! Check the linear algebra playlist.
Thank You!🥰🥰
Thanks
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.?
Thank you so much professor for your explanation. Good luck
Perfect
Professor Dave rocks🤘🤘
Great explanation! Thanks!
excellent sir
Nice explain sir i love it😍❤
Linear Algebra - Ego = Professor Dave. You are fantastic. Thank you.
Your teachings are so awesome sir thankyou
How did you just make me understand this so easily :D
very clear explanation!
Is there only two videos relating to the eigen topic?
why do they choose the value of x2 = 1 for that equation?
It really helps me! Thanks a lot!
thank you so much!!!!
very clear, thank you
Great explanation sir
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
it has no impact as long as the order of your eigenvalues and eigenvectors correspond which you seem to have done right
Wow thank you, I finally understood this stuff
Super video!
what is the rule behind choosing x2 to equal 1?
excellent explanation
Can't thank you enough.
Great explanation
I go to class for attendance and come here for the material.
Thank u professor
God Bless you Sir
thnak you so much
Damn, your videos are so great....
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]
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.
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.
Thank you so much 🔥❤️perfect explanation 💯
Thanks so much prof
How do you know which eigen vector to use first and second to make up the eigen vector matrix?
Thank you so much Sir.../\ It is so easy to understand your explanations Sir...
you're amazing thank you so much
I love your content so much !
what if for 3 by 3 matrices I got 2 lemda value then how to solve that problem?
Hi, do you have a video to explain why this works?
Please make a video on exponential matrix
thanks sir
Really talented.keep it up.