as a native french speaker, I understand your videos better than most of any french courses I've read / watched ! Thanks a lot, you save me a lot of time and desperation :D
hate it. Seems more theory rather than intuition. Let alone super rigorous dumbed down overrated book such as axler's. All students would end up doing would be memorizing them for the sake of getting through all the complexity since the intuition is nowhere to be found
I have searched and searched for an explanation like this one, took me months to finally found an explanation that anyone can understand. You are a talented teacher, thank you!
You have not just made my day but my career. I have following you for two days and seems u just keep cracking the rocket science. Am doing an Msc Data Science. Thank u so much
I've been learning eigen values and vectors solved a bunch of problems without even understanding what i was doing....Thanks a lot for that explanation!!!
last 30 secs taught me more than last 3 months. Thanks you sir. Your way of teaching is impeccable. I am absolutely stunned by the last minute intution.MIND = BLOWN
Just came across your channel .. Your videos are absolutely amazing! I'm in a multivariate analysis course, where I need to refresh my linear algebra skills, so these videos are really helpful.
How this man has not blown up bigger that someone like blackpenredpen is beyond me. I am in Calculus II right now, and this video made perfect sense to me.
These are awesome videos! They really Intuitively connect theoretical concepts in linear algebra with application in ways that I was never explicitly taught! Keep up the great work!
Your presentation skills are top-notch. Since this is the first of your videos I've watched, I don't yet know whether you devote another video to other properties of eigenvectors. You stress the collinearity, but don't talk about the way the hypervolume of some set of vectors collapses. Maybe you do this in a video where you define the determinant. Maybe your mentioning the null space of the matrix covers this. At any rate, I'll say at this point that I'll probably find all your presentations worthwhile. Best wishes in growing your channel.
I haven’t had a reason to dive into this kind of topic for over 20 years: only saw it during undergrad & grad school. But I enjoyed your technique of going through it.
I have a quick question, at 1:01 you mention that lambda is such that it is a real number, can't this be extended to imaginary numbers as well? Btw, Thanks for you great work!
I think it's important to point out what an operator can do to a vector (A*x) in general, and then point out that these eigen directions are special, because here the operator's effect is just scaling. And this is useful, because...
funny how the mathematical understanding behind it is very important to grasp, however we will never have to calculate the eigenvectors and values by hand after university.
Take the last section of the video, knowing that eigen is a German word for "own" and you will never forget what is the importance of eigenvalues and eigenvectors.
How does this property of a vector (eigen vector) remains in the same dimension even after transformation (by A) helps in some problem solving (related to ML)?
Good explanation of the math. But for 40 years I still struggle with what eigenvalues really are. Your fish example was better than most I have heard but I am still missing something vital.
It's definitely a tricky concept and I'm glad this video helped a little bit. Took me a long time to understand too. I think the easiest explanation is that an eigenvector is one where the matrix will map a vector to a multiple of itself (so that the input vector and the output vector both point in the same direction). Why does this matter? Because the same direction ensures the same ratios between each individual vector component which loosely means that the input and output vectors have the same proportions.
@@ritvikmath That helps. I have come across it in PCA and in quantum mechanics. (Yes, I am eclectic). Another question: do eigenvalues HAVE to be real?
In aerodrums screens eigen vector and eigenvalues for different landing planes may be manipulated with out collision by having graphics accordingly correct? That might have been a better explanation.
Imagine squishing or stretching a balloon by pressing on it. Certain parts of the balloon will always expand in specific directions, even if the whole shape changes-that’s like how eigenvectors and eigenvalues show up when transformations are applied. So, eigenvectors give us those "directions that don’t change direction," and eigenvalues tell us how much things get stretched or shrunk along those directions! Simple Example -- Suppose we have a dataset with information on height and weight for a group of people. By calculating the eigenvectors and eigenvalues of this dataset, we can: Find the direction in which height and weight are most correlated (an eigenvector showing the pattern). See how important this correlation is with an eigenvalue, which tells us if this pattern captures a big or small portion of the data's overall "shape."
hey, can we subtract the mean of each column from the column so as to make it zero mean before calculating the cov matrix. and in some textbooks it is divided by n-1 instead of n. why is that? Thanks
It is because of the difference between "population" and "sample" if you use for population then the accuracy must be considered so that we use n-1 it's for more accuracy.
Math and engineering classes always seem to treat Ax = λx as an abstraction. I wish someone would say at the beginning of the discussion that Ax = λx means that an eigenvector is a vector that points in the same direction after it's been operated on by A.
@@s25412 My comment about direction was a generality. Of course, A might transform x so that it points in the opposite direction, but the eigenvector will point along the same line as it was pointing before being operated on by A. A scalar multiple of an eigenvector is also an eigenvector.
very simply put idea of Eigen vectors, but there's a significant point missed about how you can even write a transformation that transforms vector in direction and scale replaced by just scaling a vector(eigen vector) by a value(Eigen value). I saw this explaination on khan academy's yt channel. th-cam.com/video/QOTjdgmNqlg/w-d-xo.htmlsi=bEgKfKdgnwz5Qy2X
as a native french speaker, I understand your videos better than most of any french courses I've read / watched ! Thanks a lot, you save me a lot of time and desperation :D
Je suis heureux d'aider! (Sorry I only took 3 years of french in high school 😁)
Last 2-3 mins are invaluable, I knew eigen values and eigenvectors but didnt know where to use them. Thanks very much!
Same here, cheers to the author of the video!
And the best explanation eigenvector/value prize goes to.... this guy!... good job man ...great video
You are amazing ... anyone who is watching this video please don't miss last few minutes.
You have an easy, inclusive and coherent way of teaching. Great job!!👌
Thank you! 😃
*me learning linear algebra for the first time even though i passed the class three or four years ago*
Oof
lol
hate it. Seems more theory rather than intuition. Let alone super rigorous dumbed down overrated book such as axler's. All students would end up doing would be memorizing them for the sake of getting through all the complexity since the intuition is nowhere to be found
I have searched and searched for an explanation like this one, took me months to finally found an explanation that anyone can understand. You are a talented teacher, thank you!
there's a really old maths book by Bostock and Chandler that has a good explanation of this too.
You have not just made my day but my career. I have following you for two days and seems u just keep cracking the rocket science. Am doing an Msc Data Science. Thank u so much
I've been learning eigen values and vectors solved a bunch of problems without even understanding what i was doing....Thanks a lot for that explanation!!!
last 30 secs taught me more than last 3 months. Thanks you sir. Your way of teaching is impeccable. I am absolutely stunned by the last minute intution.MIND = BLOWN
Great to hear!
Just came across your channel .. Your videos are absolutely amazing! I'm in a multivariate analysis course, where I need to refresh my linear algebra skills, so these videos are really helpful.
No problem!
which analysis course you doing?
Many thanks. You summarised important chapter of linear Algebra in just less than 12 minutes.
This is way better than the explanation I had in my linear algebra course long ago!
Really did a good job man. Appreciate your time and valuable information
Thank you! I took linear over a year ago and your explanations clear up so many questions I had.
Great to hear!
You not only explained the math operations, but thanks for the insite of why we are doingit. Thanks for the enlightment.
No problem!
How this man has not blown up bigger that someone like blackpenredpen is beyond me. I am in Calculus II right now, and this video made perfect sense to me.
That's the goal :)
Just came to your vids by accident.. now I'm asking how I could not have got here earlier..!
It would be useful to be able to like these videos more than once to express how appreciated they are for a newbie! Thank you!
These are awesome videos! They really Intuitively connect theoretical concepts in linear algebra with application in ways that I was never explicitly taught! Keep up the great work!
this just made me so happy... THANK U!
Your presentation skills are top-notch. Since this is the first of your videos I've watched, I don't yet know whether you devote another video to other properties of eigenvectors. You stress the collinearity, but don't talk about the way the hypervolume of some set of vectors collapses. Maybe you do this in a video where you define the determinant. Maybe your mentioning the null space of the matrix covers this. At any rate, I'll say at this point that I'll probably find all your presentations worthwhile. Best wishes in growing your channel.
I love your videos .. super helpful not just to refresh the knowledge but also understand it in a more intuitive way!! Thank you so much !
No problem!
You are good. I knew some linear algebra but I couldn't get the "feel" of it. Watching this Data Science Basics series has changed it.
I haven’t had a reason to dive into this kind of topic for over 20 years: only saw it during undergrad & grad school. But I enjoyed your technique of going through it.
Thanks!
11:35 useful to think about the same "ratio", thank you boss
Excellent explanation. Very useful in my mathematical modelling of infectious disease learning. Thank you
You're helping me a lot refreshing these concepts! So happy I found your channel!
Awesome! Thank you!
this cleared up so much and importance of why we need eigenvectors, tysm!!
Wow, I don’t know why professors rarely provide motivation like this.
This man is a real gem.
I appreciate you making these videos as they have helped so much in understanding abstract machine learning/data science concepts! :) Cheers to you!
Cheers to me . I taught him
What an amazing example in eigenvector. Help fish to find fish with same "figures". Surely has been used in dating apps😂
Your videos are absolutely top-notch. Keep it up!
I have a quick question, at 1:01 you mention that lambda is such that it is a real number, can't this be extended to imaginary numbers as well? Btw, Thanks for you great work!
Yes.
thank you, I learned faster and easier with your explanation, you rock!
Lovely! I have a question: if the scalar (eigenvalue) is negative, when multiplied is the vector's direction not changed by 180 degrees?
Very clean and clear presentation.
this video made it all look so so simple, thankyou very much!
You are a literally a Godsend and a savior, Machine Learning is becoming more clear with every video i watch of you fam, thank you!
2:51 Thank you. A teacher who melds big pictures with equations
Awesome splendid mesmerising
Which video to follow for the importance of invertibility?
This is amazing! Thank you so much for making these videos.
I'm taking CS229 and it helps a lot, thank you!
Thank you, really helpful, awesome explanation :)
Best video on eigen
I think it's important to point out what an operator can do to a vector (A*x) in general, and then point out that these eigen directions are special, because here the operator's effect is just scaling. And this is useful, because...
Killed it. Period.
How did u assume the shape of X was (2,1)?
Was it because of two eigen values?
really nice explanation thank you!!
great explanation. thanks.
just found you & I LOVE YOU
Hey, special thanks for that last application example 😊
WOW!! bless you man🌺
Thanks man! Really good explanation! Keep it up!
Thanks, will do!
God Tier Explanation
thank you I love this topic it gives me a lot in the foundation of basic data science most likely in machine learning
This is amazing. You are amazing.
thanks!
funny how the mathematical understanding behind it is very important to grasp, however we will never have to calculate the eigenvectors and values by hand after university.
Thank you for this great explanation .
Glad it was helpful!
Great video!
Take the last section of the video, knowing that eigen is a German word for "own" and you will never forget what is the importance of eigenvalues and eigenvectors.
How does this property of a vector (eigen vector) remains in the same dimension even after transformation (by A) helps in some problem solving (related to ML)?
This helps a lot!! Thank you so much
Explanation is awesome
Good explanation of the math. But for 40 years I still struggle with what eigenvalues really are. Your fish example was better than most I have heard but I am still missing something vital.
It's definitely a tricky concept and I'm glad this video helped a little bit. Took me a long time to understand too. I think the easiest explanation is that an eigenvector is one where the matrix will map a vector to a multiple of itself (so that the input vector and the output vector both point in the same direction). Why does this matter? Because the same direction ensures the same ratios between each individual vector component which loosely means that the input and output vectors have the same proportions.
@@ritvikmath That helps. I have come across it in PCA and in quantum mechanics. (Yes, I am eclectic).
Another question: do eigenvalues HAVE to be real?
These videos are amazing!
why are there only 2 items in the x column vector?
In aerodrums screens eigen vector and eigenvalues for different landing planes may be manipulated with out collision by having graphics accordingly correct? That might have been a better explanation.
Thanks for your clear explanation
great job
great explanation!!
Thank you very well explained and I like the fish analogy. .
Good video! Thanks.
Could you upload a video on Hat Matrix?
You are good 👍
Does matrix A have to be square?
amazing !!
Imagine squishing or stretching a balloon by pressing on it. Certain parts of the balloon will always expand in specific directions, even if the whole shape changes-that’s like how eigenvectors and eigenvalues show up when transformations are applied.
So, eigenvectors give us those "directions that don’t change direction," and eigenvalues tell us how much things get stretched or shrunk along those directions!
Simple Example --
Suppose we have a dataset with information on height and weight for a group of people. By calculating the eigenvectors and eigenvalues of this dataset, we can:
Find the direction in which height and weight are most correlated (an eigenvector showing the pattern).
See how important this correlation is with an eigenvalue, which tells us if this pattern captures a big or small portion of the data's overall "shape."
my man gave the fish a mohawk :))) thanks for the content though. much love
soooo good！
so we always gonna use only one eigenvalues, am I right?
Please continue making data science related math videos
that's the plan !
I just subscribed!
yay! thanks :)
Fantastic
Thank you
hey, can we subtract the mean of each column from the column so as to make it zero mean before calculating the cov matrix. and in some textbooks it is divided by n-1 instead of n. why is that? Thanks
I think because with (n-1) the estimator is unbiased...
It is because of the difference between "population" and "sample" if you use for population then the accuracy must be considered so that we use n-1 it's for more accuracy.
Talking about fishy vectors... 8:31
thank you soooo much
You're welcome!
does Ax = LAMDA X holds for all x?
Nope
Evals and Evecs are everywhere in DS
great fish !
haha thanks!
Math and engineering classes always seem to treat Ax = λx as an abstraction. I wish someone would say at the beginning of the discussion that Ax = λx means that an eigenvector is a vector that points in the same direction after it's been operated on by A.
they could point in different direction though, is lamda is a negative number
@@s25412 My comment about direction was a generality. Of course, A might transform x so that it points in the opposite direction, but the eigenvector will point along the same line as it was pointing before being operated on by A. A scalar multiple of an eigenvector is also an eigenvector.
@@robertpenoyer9998 Thank you
新たに定理を発見しました。
very simply put idea of Eigen vectors, but there's a significant point missed about how you can even write a transformation that transforms vector in direction and scale replaced by just scaling a vector(eigen vector) by a value(Eigen value). I saw this explaination on khan academy's yt channel.
th-cam.com/video/QOTjdgmNqlg/w-d-xo.htmlsi=bEgKfKdgnwz5Qy2X
🌹🌹🌹
🌹 🌹 🌹
Didn't really go over finding the Eigenvector 😕 just solved the system of equations and left it be.
Why couldn’t you have been my teacher when I was studying eigenvectors. Sigh.
Hi, could you please do the computation for eigen value -2 and eager to know how to plug in x1 and x2