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!
I am from South Africa, because of you i have managed to get My Degree. Thank you so much
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.
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 :)
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)
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.
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.
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 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.
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.?
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.
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
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.
For the Checking Comprehension part, for the X I got: 2 4 4 4 And so when calculating X D X^-1 I got: -6/3 1/3 -2/3 -3/3 I'd only achieve the same result for initial matrix A if I multiply that last matrix that I got with -1/3. Is it still considered correct?
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?
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!
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
Congratulations professor Dave for becoming a father!
Did he really ?😮
late...
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.
Lemme hit🤤
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 is always a hard topic to teach. This is straight forward and clear. Great video!
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!
7:41 "so, lets check comprehension" wowww, never seen that part in any other video. awesome, thanks a lot for including that :)
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 :])
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.
XD
@@chimphead73 LOL!!!!!!!!!!!
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.
You're such an incredible teacher! Textbooks are so esoteric where your videos are so accessible :) thank you for your work
thank you professor.
every teacher must see you videos first to be qualified for teaching
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
Professor Dave will go down in history as one of the greatest legends of all time.
Hi Professor Dave! You helped me sooo much before my test! U saved me and my classmates!
This definitely simplified everything that was taught to me in my class lecture. Everything is super clear now. Thank you so much!
كل مرة بحضر فيديوهات للبروفيسور بطلع فاهمه، طريقته بالشرح مثالية
، ممتنه جدا
4:13 , why did you choose x2 = 1, why not x1 = 1?
If we take x1 = 1 will our answer be the same ?
Universities around the world NEED professor like you.
Taught the entire concept so easily. WAY BETTER THAN MY T100 UNI LECTURER
Congratulations for you job, Professor Davis. You make mathematics easy to understand. I wish you were my teacher.
My brain hurts
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 :)
@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 ?
Did you get your answer?
You saved me a lot of time Dave. Thanks for the incredible video series.
This is indeed a pure gem! Thank you for posting it 👏
Thanks Mr Dave for making the topic so easy😊
Your videos are excellen. In my native language: Sus vídeos son excelentes. Thanks a lot
sus
This was honestly so good. Thank you.
loved the video. thank you for saving my academics.
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
i m from kerala , india
Well class
Thank you sir,
☺️
I'm from tamilnadu 😂
I don't understand anything 🤯😭😭
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.
Thanm you so much sir.. This is another vedio I understood whole concept from you.. you are such a prolific teacher.. Wooh!
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.
Where was this series the beginning of the semester? I now have to cram so much information the days before my final.
great explanation. Thank you so much
Professor Dave rocks🤘🤘
Bro saved my life.
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.
P.S. in 6:45 ( A= X-1 D X ) is known as eigenvalue decomposition
Nice explain sir i love it😍❤
Sir, you saved my life
Professor Dave casually saving everyone's ass again this year
Thank you so much , this is the best i’ve found !
Great explanation sir
You are so good at what you do. i hope I become like you in terms of teaching! So cool!
Thank you! I can't understand why professors complicate things so much!
Please why do you normally choose X2=1
I don’t get that part
Thank you so much professor for your explanation. Good luck
Your teachings are so awesome sir thankyou
amazing how an 8 minute video explains everything that an university teacher cant in 2 hours
Great explanation! Thanks!
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...
very clear explanation!
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.
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.?
excellent explanation
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.
How did you just make me understand this so easily :D
great explaination
Really talented.keep it up.
Thank you so much 🔥❤️perfect explanation 💯
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
I love your content so much !
Wow thank you, I finally understood this stuff
It really helps me! Thanks a lot!
Thank You!🥰🥰
you're amazing thank you so much
I love you you're a lifesaver!
very clear, thank you
amazing I understand BST ❤ thnks
6:52 why did he multiply DX^-1 first instead of XD?
It doesn't matter you will get the same answer...
Thanks so much prof
excellent sir
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 professor dave
Just thank you
You are saving me from failing my math class
Appreciated God bless u man
For the Checking Comprehension part, for the X I got:
2 4
4 4
And so when calculating X D X^-1 I got:
-6/3 1/3
-2/3 -3/3
I'd only achieve the same result for initial matrix A if I multiply that last matrix that I got with -1/3. Is it still considered correct?
Super video!
Thank you so much Sir.../\ It is so easy to understand your explanations 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
Linear Algebra - Ego = Professor Dave. You are fantastic. Thank you.
Great Professor
thank you so much!!!!
God Bless you Sir
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
Please make a video on exponential matrix
what is the rule behind choosing x2 to equal 1?
Thank u professor
Thanks
thank you so much!
u the goat fr
Damn, your videos are so great....
Perfect