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!
Congratulations for you job, Professor Davis. You make mathematics easy to understand. I wish you were my teacher.
3 года назад+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.
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.
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
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.
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.
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.?
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?
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
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...
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.
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)
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?
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.
Prof when i try the example in the end the inverse reads -1,-2,-2 and -2 since we multiplied X by -2...I have been stuck on this for hours..can you please explain it?
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?
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?
sir in integration video you say that we can find the area of a curve by slipting into a bunch of rectangles a mountain has a curve shape, can we split it in to a bunch of rectangles, please reply
yes, the rectangles are infinitely thin so they are essentially lines, but it would be nearly impossible to find a function that corresponds with the topology of a mountain so i don't think it's really meant for that application
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]
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.
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?
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.
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 💯
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
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!
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
This definitely simplified everything that was taught to me in my class lecture. Everything is super clear now. Thank you so much!
You're such an incredible teacher! Textbooks are so esoteric where your videos are so accessible :) thank you for your work
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!
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.
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!!!
Congratulations for you job, Professor Davis. You make mathematics easy to understand. I wish you were my teacher.
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.
Hi Professor Dave! You helped me sooo much before my test! U saved me and my classmates!
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 :)
You saved me a lot of time Dave. Thanks for the incredible video series.
I am from South Africa, because of you i have managed to get My Degree. Thank you so much
Professor Dave will go down in history as one of the greatest legends of all time.
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.
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.
You are so good at what you do. i hope I become like you in terms of teaching! So cool!
This is indeed a pure gem! Thank you for posting it 👏
This was honestly so good. Thank you.
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
great explanation. Thank you so much
7:41 "so, lets check comprehension" wowww, never seen that part in any other video. awesome, thanks a lot for including that :)
Thank you so much professor for your explanation. Good luck
loved the video. thank you for saving my academics.
Thanks Mr Dave for making the topic so easy😊
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!!!!!!!!!!!
thank you professor.
every teacher must see you videos first to be qualified for teaching
Thank you so much , this is the best i’ve found !
Universities around the world NEED professor like you.
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.
Your teachings are so awesome sir thankyou
Thanm you so much sir.. This is another vedio I understood whole concept from you.. you are such a prolific teacher.. Wooh!
@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 ?
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.?
It really helps me! Thanks a lot!
Great explanation! Thanks!
Thank you! I can't understand why professors complicate things so much!
Where was this series the beginning of the semester? I now have to cram so much information the days before my final.
very clear explanation!
Thank you so much Sir.../\ It is so easy to understand your explanations Sir...
Thank you so much 🔥❤️perfect explanation 💯
Your videos are excellen. In my native language: Sus vídeos son excelentes. Thanks a lot
sus
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?
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
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.
How do you know which eigen vector to use first and second to make up the eigen vector matrix?
thanks prof dave, although i'm lost as to how and why i need to know this for my industrial engineering diploma.
Hi, do you have a video to explain why this works?
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...
Wow thank you, I finally understood this stuff
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.
Sir, If X2 corresponds to lamda=1 and X1 corresponds to lamda=2 do we get same diagonal matrix?
best explanation i ever seen entire RUclips 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
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?
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.
Great explanation
Prof when i try the example in the end the inverse reads -1,-2,-2 and -2 since we multiplied X by -2...I have been stuck on this for hours..can you please explain it?
I love your content so much !
excellent explanation
4:13 , why did you choose x2 = 1, why not x1 = 1?
If we take x1 = 1 will our answer be the same ?
How did you just make me understand this so easily :D
Sir can I write eigen vectors at any place during making X matrix
very clear, thank you
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?
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
sir in integration video you say that we can find the area of a curve by slipting into a bunch of rectangles a mountain has a curve shape, can we split it in to a bunch of rectangles, please reply
yes, the rectangles are infinitely thin so they are essentially lines, but it would be nearly impossible to find a function that corresponds with the topology of a mountain so i don't think it's really meant for that application
P.S. in 6:45 ( A= X-1 D X ) is known as eigenvalue decomposition
Great explanation sir
professor dave, how do you know how to put the 1 and 2 in that order in the diagonal matrix?
wish he answered this
what is the rule behind choosing x2 to equal 1?
thanks alot, you are the best
Professor Dave casually saving everyone's ass again this year
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]
Thank you professor dave
Just thank you
You are saving me from failing my math class
great explaination
Nice explain sir i love it😍❤
Thanks so much prof
you're amazing thank you so much
Really talented.keep it up.
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.
Check the earlier tutorial on eigenvalues and eigenvectors.
Can you do for a 3x3 matrix
can my D X be in a different order as long as their eigen value/vectors are in the same order respectively to each other?
Yes.
Perfect
God Bless you Sir
thank you so much!
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?
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.
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?
Thank You!🥰🥰
Please make a video on exponential matrix
Great Professor
Professor Dave rocks🤘🤘
THANK YOU
Please why do you normally choose X2=1
I don’t get that part
Can't thank you enough.
Sir, you saved my life