Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!
How did you found adjoint of 2x2 matrix youre moving very fast at 8:20 finding B matrix? Because its equal to zero matrix please reply fast i have exam two days later
you are the only reason I am able to pass calculus and linear algebra. My teachers are great, but for some reason this "one on one" examples are really what gets me to understand it.
Its because he's too the point and writes things in steps, like i was watching some other videos of people explaining this and there just waffling on and jumping between things without explaining them as if the person has done them before. There isn't really much excuse when your doing it by a video because you can prepare the most key and important points and how to say it, before doing the video.
Every time I have written a Linear Algebra and Calculus I & II exams/tests, I always get a, "What did patrickJMT teach me?" moment. I'm probably going to have those brilliant moments for the next 4 years... Then I will come back to this same video and thank you for catapulting me into graduation day with a degree in Mechanical Engineering.
University professors are not there to teach you. They are there to provide you with material that you should already know. University isn't high school.
I like how you do math, you know how to explain it in steps, I wish my instructor can work in step, thank you so much patrick, God will reward you my friend.
It's 2am, I have a test at 9am. There will be literally 2 questions on a 2x2 matrix. 1. Find the eigenvalues of this matrix 2. Find the eigenvectors of this matrix. This video wins the internet.
Dear Sir, I sincerely thank you for taking the effort to create such useful videos. I was reading through my notes and textbook till i began to panic. I have an exam in 2 days time and I would no have understood this topic if it were not for your kind help. Best regards from Singapore.
I know this video is 9 years old but even to this day you are helping others including me to achieve their goals in college and actually aid them in understanding fascinating mathematical topics. Thank you and I wish you well :)
I will never understand why so many professors are unable to explain what a theorem states and then go on to give a simple step by step answer like this
也许，这些理论在某些教授的理解能力中，还不是十分清晰的。思路未清，词即难达。 Maybe,some professors have not get the clear understanding in their mind. No one can explain more clearly than he think.
I think that since they have done it so many times, and have realized the importance of the _concept_, they focus so much on the theorem and not on the operation. It is important, but a lots of times you understand the importance and _can use it_ after you are familiar with SEVERAL tools. One day, they just click and understand them better. That's not the situation that students are in, they ask us to remember lots of things that stack upon each other to build new things and they tell us "this (ALL) is important"... well, we (still) not care, we don't have the tools to care either.
I read so many ****ing tutorials online explaining this concept, none of them came as clearly as yours. Thank you for contributing knowledge to the public.
I've been trying so hard to understand this! I really understand math when someone explains it step by step to me. I was stuck after getting the eigen values and never knew all you have to do was assume a value for x1 or x2. You helped me out a lot!
All of your videos are very helpful, and I recommend your channel to all my fellow engineering student friends. Thank you for creating all of your videos.
Thank you so much for taking your own time and energy into making these videos. You have helped understand so much more then my teacher and a lot faster. I just wanted to say thank for all the hard work you put in to help people like me out. Your awesome!
got a maths resit tomorrow and this video has saved my life, the lecturer that teaches me maths made this so much more complicated then it needs to be, so thank you!!
We all just need to subscribe to your future youtube sessions rather than wasting money and time only to feel totally confused and sleepy in University class learning about these...Thanks Patrick. You are a legend!
I've never commented on a RUclips Video before. But this right here is just amazing. Thank you. My professors make it feel impossible. Thank you so much. I'll open all the videos you made, and see the ads. You deserve it.
lol i had a three decimal eigenvalues. and had to do inverse off a 5x5. not terrible but he wanted adj(5x5)/det(5x5). This means that ill end up having to find the det of 25 4x4 matricies
Prior to opening this video, I'd spent the past 2 hours fruitlessly trying to understand this topic using textbooks. 10 minutes here and I understand already, thank you.
I was bad at math since I was in junior high school. During my first semester in university, I found this guy's videos and watched them to help myself get over the calculus classes. Today I am taking my last undergrad final exam, and I am still watching his videos. And perhaps I will come back to watch the videos after two months when the graduate school begins
Thank you for this clear and helpful refresher! If you ever have the time, it would be great to see some videos explaining related applications of linear algebra in data science, like PCA and SVD. It’s hard to find clear, succinct explanations for them!
+patrickJMT Hey Patrick. For the first problem with eigenvalue T = 8, you used a row reduction method for finding the vector x. In doing so, you made the second row of the matrix have all zeros...BUT for the second eigenvalue T = -2, you made the first row have all zeros. Can you explain why you used that method and didn't use the same row in both cases?
For the eigenvalue -2, I divided the top row by 3 so instead of 9 and 3 on the top, I ended up with 3 and 1. From there you can do Row1-Row2 and get (3,1) on top and (0,0) on bottom row.
Sorry for the late reply but it may help others: You pick numbers that reduce the bottom row to zero, here 3*R1 is the same as -R2 so by adding them together they cancel out, giving the desired zero on the bottom row.
@@seansethi196 It ultimately doesn't matter, because you just need one any one eigenvector. Remember, any non-zero scalar multiple of an eigenvector is also an eigenvector for a particular eigenvalue.
Finding the Eigenvector from 6:00 to 8:25 is a bit confusing, namely the row reduction and seemingly arbitrary picking of values for x1 and x2. I tried to do it step by step with another problem. I get lost there. Can't find the Eigenvectors :(
Instead of thinking of the problem as: Find THE eigenvector. Reword it to: Find AN eigenvector. When he gets the matrix into Reduced Row Echelon Form, - research this to understand why we row reduce - any real number we plug into the equation he writes at 7:43 for x1 or x2(only pick a number for 1 value and solve for the other) can reduce to {3 1} like he got, so that's why its an arbitrary selection. Try it!
you teach better than my Prof, you teach better than the author who wrote the textbook. Your videos give me hope to ace my final exam! Thank you so much sir
your videos are simple and understandable thank you. just a question how did you pick x2=1? is it because 1 and 3 are within the matrix or can we chose any number?
@@shirashira8871 got the answer ! you can see in others comments : "ultimately doesn't matter, because you just need one any one eigenvector. Remember, any non-zero scalar multiple of an eigenvector is also an eigenvector for a particular eigenvalue."
I don't like how i explained that... let me do it again. Once you find the relation between x2 and x1 it doesnt matter what numbers you chose. You may pick any x1 to get a corresponding x2.
ah okay, thank you so much I've thought about It but I was uncertain, thank you so much for your answers, and sorry If I make english misspellings, I'm moroccan and we study In french
bob butts Love the explanation. You had it all messed up at first but you came back with the second post and cleared it up. You could have left it all messed up and probably nobody would have noticed but you came back... You came back. God damn you got a bright future. Best of luck in future endeavors and shout out to any who enjoys linear algebra
@@aussiecomrade5972 There is a subspace of eigenvectors with x1 and x2 corresponding (or relational) entries. (orignal matrix) * (subspace of eigen vectors that you choose from)= (eigenvalue) * (eigenvector chosen).
I never understood this when my lecturer taught me.. but after watching your video, I got a clearer view and understanding about the course.. thanks for the explanation 🙌
@@peterlee5726 In typical University Linear Algebra classes, we have to reduce our matrices manually. This can easily be done in most calculators or something like MATLAB.
Thank you so much for breaking this process down in such detail. It really helped me understand what was going on for more complex and high n matrices in the course I'm taking.
I'm assuming ur stuck after you've written down det(A-lambda times I). Go back to your notes on calculating the determinant of a 3x3 matrix. It's just a bunch of tedious calculations at that point, and you end up with a cubic equation which of course is a little more difficult to factor to determine the 3 roots which then give you 3 eigenvalues. Then its just a matter of substitution as Patrick showed you to get the eigenvectors.
Jesus Christ, you explained this in such a clear and precise manner that I managed to understand what my professor took over an hour to explain in under 15 minutes
I echo the comments below; great videos on this topic! I took LA 3 years ago and I didn't realize how much review I would get on determinants, row reduction, etc. Thanks!!
You actually teach properly, I did all this in my A-levels, and going into 2nd year of uni I'm brushing up on it. You go into the right amount of detail necessary and don't take what I'm predicting to be 3 lectures (150mins) to get there :P thanks
Thanks for this video. I was stuck at the part of how to determine the eigenvectors, and your video cleared it up for me. I really appreciate it! Keep the good work!
This helped me understand what "diagonalizing" a 2x2 matrix for the schroedinger equation actually meant in my Solid State Physics class so THANK YOU!!!
![I.N "HALLUCINATION" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/n5B5q1Hwt_U/mqdefault.jpg)
Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other!
Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!
Please definitely post a 3x3 example! This is super helpful.
Can you generalize discuss the implications of the cases where the eigenvalues come out as imaginary?
How did you found adjoint of 2x2 matrix youre moving very fast at 8:20 finding B matrix? Because its equal to zero matrix please reply fast i have exam two days later
Do we have to follow all these steps or is there a faster way to go about it?
Please take an example of solving 3×3 matrix too
I have litterally skipped 80% of my linear algebra class this semester and have over an 85% solely based on studying from your videos.. I love you man
Just did the same with an exam coming up in 2 weeks. Why do we do these things to our self?!?
LMAO!.
@@KH-ft4ut Exactly.. My exam is in just after 2 weeks and I ve started to look at things just now
@@Sam-wt1cx Good luck mate, I passed my exam. But I still have no idea what Eigenvalues or eigenvectors are actually useful for.
The Duke lol I guess I’m lucky my professor is not bad although these videos help me out cuz I’m taking two math classes and I get confused at times.
Do you ever think about how many people you've helped become engineers or scientist? You are really doing humanity a great cause my friend, thank you!
+The Visionary I'm sure I've helped a few here and there :)
you are the only reason I am able to pass calculus and linear algebra. My teachers are great, but for some reason this "one on one" examples are really what gets me to understand it.
Its because he's too the point and writes things in steps, like i was watching some other videos of people explaining this and there just waffling on and jumping between things without explaining them as if the person has done them before.
There isn't really much excuse when your doing it by a video because you can prepare the most key and important points and how to say it, before doing the video.
Every time I have written a Linear Algebra and Calculus I & II exams/tests, I always get a, "What did patrickJMT teach me?" moment. I'm probably going to have those brilliant moments for the next 4 years...
Then I will come back to this same video and thank you for catapulting me into graduation day with a degree in Mechanical Engineering.
hey where are you studying Mechanical Engineering >
..
Im studying it At the University of Guyana
let me just say... you are single handedly saving me this semester.
Literally !
fools cant even explain this in an hour. patrickjmt is a beast.
When they explain this stuff in an hour they just rush through it and don't explain anything, Patrick is a life saver
Eric Da Silva Uni profs are usless bro
i guess thats why there's that saying "those who can, do; those who can't, teach"
Yea seriously if it weren't for patrickjmt and other RUclipsers I would have no idea wtf is going on in my diff eq class.
University professors are not there to teach you. They are there to provide you with material that you should already know. University isn't high school.
I like how you do math, you know how to explain it in steps, I wish my instructor can work in step, thank you so much patrick, God will reward you my friend.
i am already rewarded by feeling appreciated in this world as your comment does for me ;)
Angelo Ungery the best regards and best wishes
You helped me in 12th grade with AP calculus and now you're helping me as a senior in college. Thank you my friend
It's 2am, I have a test at 9am. There will be literally 2 questions on a 2x2 matrix. 1. Find the eigenvalues of this matrix 2. Find the eigenvectors of this matrix. This video wins the internet.
+Allegro Crab introductory ?Linear algebra?
+Allegro Crab It's currently 1:15am here, my exam is 9am. I can relate :P
HaydenMcM1
you're australian too? good luck m8.
***** Yep, thanks mate :)
its already 2016 but I can relate to what you said. its 2am and I have my exams later at 9am. 😂😂
You sir, are a God amongst men. Thank you for these videos, you legend.
+Flambe nah, just a normal guy trying to help in the best way i know how!
+patrickJMT JOHN 8:32 :) #lifeabove
+Flambe I don't think it's right comparing him to god. I mean he's good... but he's no Patrick.
definitely a god among men
Dear Sir, I sincerely thank you for taking the effort to create such useful videos. I was reading through my notes and textbook till i began to panic. I have an exam in 2 days time and I would no have understood this topic if it were not for your kind help. Best regards from Singapore.
I know this video is 9 years old but even to this day you are helping others including me to achieve their goals in college and actually aid them in understanding fascinating mathematical topics. Thank you and I wish you well :)
I will never understand why so many professors are unable to explain what a theorem states and then go on to give a simple step by step answer like this
也许，这些理论在某些教授的理解能力中，还不是十分清晰的。思路未清，词即难达。
Maybe,some professors have not get the clear understanding in their mind. No one can explain more clearly than he think.
I think that since they have done it so many times, and have realized the importance of the _concept_, they focus so much on the theorem and not on the operation.
It is important, but a lots of times you understand the importance and _can use it_ after you are familiar with SEVERAL tools. One day, they just click and understand them better.
That's not the situation that students are in, they ask us to remember lots of things that stack upon each other to build new things and they tell us "this (ALL) is important"... well, we (still) not care, we don't have the tools to care either.
I read so many ****ing tutorials online explaining this concept, none of them came as clearly as yours. Thank you for contributing knowledge to the public.
May I ask for an application example for Eigenvectors and Eigenvalues such as Page Rank algorithm?
I've been trying so hard to understand this! I really understand math when someone explains it step by step to me. I was stuck after getting the eigen values and never knew all you have to do was assume a value for x1 or x2. You helped me out a lot!
doing maths along listening to your videos is blissful!
Ha, glad you feel that way!
All of your videos are very helpful, and I recommend your channel to all my fellow engineering student friends. Thank you for creating all of your videos.
i must admit that left handed people are always somehow gifted and special. thanks for helping man !!
Thank you so much for taking your own time and energy into making these videos. You have helped understand so much more then my teacher and a lot faster. I just wanted to say thank for all the hard work you put in to help people like me out. Your awesome!
got a maths resit tomorrow and this video has saved my life, the lecturer that teaches me maths made this so much more complicated then it needs to be, so thank you!!
Is there a word more than thank you.ahh I appreciate this. no there must be something better. You are a complete University.
We all just need to subscribe to your future youtube sessions rather than wasting money and time only to feel totally confused and sleepy in University class learning about these...Thanks Patrick. You are a legend!
Thanks for the video, sorry, can You please explain how you came to 3R1+R2 >R2 when determining the eigenvectors? Thank you in advance
I've never commented on a RUclips Video before. But this right here is just amazing. Thank you. My professors make it feel impossible. Thank you so much. I'll open all the videos you made, and see the ads. You deserve it.
In that case, my instructor is a masochist
+HaydenHatTrick same
Lol, I think you mean sadist, my Eigen value were 5.372 and -.372.......
+Cj Looklin Tell your professor to screw off. I feel so sorry for you
lol i had a three decimal eigenvalues. and had to do inverse off a 5x5. not terrible but he wanted adj(5x5)/det(5x5).
This means that ill end up having to find the det of 25 4x4 matricies
Oh noooooooooooooooooooooooooooo
You have literally helped me 4.0 all 3 calc classes, my proofs class, and now linear algebra. Thank you!
I cannot express how grateful I am for linear algebra libraries, saving me from having to do any of this
Jajaja I couldn't agree more. It's pitiful how many teachers are reluctant to integrating technology to subjects like this
I'll say it once: BEST VIDEO on this Topic!!!
I wish my physics lecturers at university had been like you.
Prior to opening this video, I'd spent the past 2 hours fruitlessly trying to understand this topic using textbooks. 10 minutes here and I understand already, thank you.
my teacher teaches a same question by very complicated method
but your method is so understandable
thnks sir :-)
I was bad at math since I was in junior high school. During my first semester in university, I found this guy's videos and watched them to help myself get over the calculus classes. Today I am taking my last undergrad final exam, and I am still watching his videos. And perhaps I will come back to watch the videos after two months when the graduate school begins
Thank you for this clear and helpful refresher! If you ever have the time, it would be great to see some videos explaining related applications of linear algebra in data science, like PCA and SVD. It’s hard to find clear, succinct explanations for them!
Without doubt the best video on the web for eigenvectors and eigenvalues. Thanks a lot this masterpiece.
You are the best at explaining! I love your videos
Thanks!
+patrickJMT Hey Patrick. For the first problem with eigenvalue T = 8, you used a row reduction method for finding the vector x. In doing so, you made the second row of the matrix have all zeros...BUT for the second eigenvalue T = -2, you made the first row have all zeros.
Can you explain why you used that method and didn't use the same row in both cases?
+JC Tutoring it's the same if you make the second row of the matrix have all zeros, you still have same result
For the eigenvalue -2, I divided the top row by 3 so instead of 9 and 3 on the top, I ended up with 3 and 1. From there you can do Row1-Row2 and get (3,1) on top and (0,0) on bottom row.
2 minutes in and im already understanding more from this than my slides from my uni website, god bless you
How did you know the “plug in values” to create the Eigenvectors? Would any number for x1 do if you multiply it by the coefficient of x2?
yes any number you can since it just a scalar. For simplicity just pick number 1.
You sir, are a lifesaver.. Finally taught in a way that I can understand fully. Great job man, and thanks.
greatest youtuber!
I've seen two video's about eigenvalues and eigenvectors and am amazed. Amazingly clear instructions.
in 7:10 you wrote 3R1+R2→R2 How do you pick exact these values ?? for row one and two
Sorry for the late reply but it may help others: You pick numbers that reduce the bottom row to zero, here 3*R1 is the same as -R2 so by adding them together they cancel out, giving the desired zero on the bottom row.
Thank you from Australia
Welcome from india
Amazing, I learn here in 5 minutes what didn't learn with my teacher in 2 hours. Keep up the good work Patrick.
When choosing a value for x1 for the eigenvectors, does it specifically need to be 1? or any value? and how do you know what value to choose?
Yeah, like you can also use the letter A for example X2= A and X1=3A
I have the exact same question, choosing 1 seemed arbitrary but I do not understand why it was chosen.
@@seansethi196 It ultimately doesn't matter, because you just need one any one eigenvector. Remember, any non-zero scalar multiple of an eigenvector is also an eigenvector for a particular eigenvalue.
@@moatef1886 appreciate the reply, thank you!
You are a legend. Brilliantly but simply explained.
Finding the Eigenvector from 6:00 to 8:25 is a bit confusing, namely the row reduction and seemingly arbitrary picking of values for x1 and x2.
I tried to do it step by step with another problem. I get lost there. Can't find the Eigenvectors :(
Instead of thinking of the problem as: Find THE eigenvector.
Reword it to: Find AN eigenvector.
When he gets the matrix into Reduced Row Echelon Form, - research this to understand why we row reduce - any real number we plug into the equation he writes at 7:43 for x1 or x2(only pick a number for 1 value and solve for the other) can reduce to {3 1} like he got, so that's why its an arbitrary selection. Try it!
@@supahotfire8886
Thanks. :) I'm out of school now but Ill try it lol. I think i did accomplish this in one of my later courses.
are you an engineer now lol@@AceofDlamonds
@@litjew6669
Hehe...i'll just say I wish I could rewind time and study computer science instead 😂
you teach better than my Prof, you teach better than the author who wrote the textbook. Your videos give me hope to ace my final exam! Thank you so much sir
Can you please put all linear algebra videos in one playlist ? that would be wonderfull but thank you Patrick!
Wow I read lots of books on this topic and now I understand it. You are the best!
Great vid, but why do you just choose any number to sub in, wouldn't you get a different value if you subbed 2 instead of 1?
You open my eyes and I can see better than before this course all this week has been making me suffer thank you
your videos are simple and understandable thank you. just a question how did you pick x2=1? is it because 1 and 3 are within the matrix or can we chose any number?
yes i want to know about this too
@@shirashira8871 I'm in the same position hahah I want to know too
@@shirashira8871 got the answer ! you can see in others comments : "ultimately doesn't matter, because you just need one any one eigenvector. Remember, any non-zero scalar multiple of an eigenvector is also an eigenvector for a particular eigenvalue."
@@sauceandalouse2624 Thank you for your explanation:)
You are the main reason why I'm passing my Math and calculus courses...Respect Math Boss
Why we let x2 = 1 I don't understand, please help
It doesn't matter what you set x2= to. you can pick any number you want because any non zero multiple of eigenvector xbar is an eigenvector
I don't like how i explained that... let me do it again. Once you find the relation between x2 and x1 it doesnt matter what numbers you chose. You may pick any x1 to get a corresponding x2.
ah okay, thank you so much I've thought about It but I was uncertain, thank you so much for your answers, and sorry If I make english misspellings, I'm moroccan and we study In french
bob butts Love the explanation. You had it all messed up at first but you came back with the second post and cleared it up. You could have left it all messed up and probably nobody would have noticed but you came back... You came back. God damn you got a bright future. Best of luck in future endeavors and shout out to any who enjoys linear algebra
@@aussiecomrade5972 There is a subspace of eigenvectors with x1 and x2 corresponding (or relational) entries.
(orignal matrix) * (subspace of eigen vectors that you choose from)= (eigenvalue) * (eigenvector chosen).
You explain everything so well, I finally understand how to find the eigenvectors!! THANK YOU!
7:10 where did the 3 come from?
3xR1 + R2 = R2
??? !!!
Can someone answer this plz????
It's a variable, i think he is using the gauss Jordan formula
he is trying to reduce it in echelon form.
I never understood this when my lecturer taught me.. but after watching your video, I got a clearer view and understanding about the course.. thanks for the explanation 🙌
I can pinpoint the exact moment when you lost me :D
7:00
Hey it's been 3 years but yeah.... WTF is row reduction?
@@peterlee5726 In typical University Linear Algebra classes, we have to reduce our matrices manually. This can easily be done in most calculators or something like MATLAB.
Peter Lee I know your comment is old, but RUclips for his video called “gauss-Jordan elimination” that’s what row reduction is
but why we need row reduction here
Could anybody explain it to me please?
Hey man you are the best. I use to watch your videos before exams.
“Unless the instructor is a real masochist” thanks for accurately describing my math teachers
In addition to the world class explanations, I appreciate the encouraging statements at the end of your videos. It really helps me to keep going.
Do you have any video on diagonalization of matrices ? Thanks for the helg witn Eigenvalues-vectors :)
I love you baby 😊😍😘😚😗😙
March 2019 and it is still very useful video, I appreciate your teaching style!
That sharpie though. So squeaky. The video is fantastic though.
Kind of a comforting sound tbh
Thank you so much for breaking this process down in such detail. It really helped me understand what was going on for more complex and high n matrices in the course I'm taking.
Doesnt that mean there are infinite eigenvectors?
Yes, once you find an eigenvector, any scalar multiple of that vector will also be an eigenvector.
You're a good soul! I have benefited from many of your videos. Thanks for the help!
You think you can do a 3x3 matrix?
I'm assuming ur stuck after you've written down det(A-lambda times I). Go back to your notes on calculating the determinant of a 3x3 matrix. It's just a bunch of tedious calculations at that point, and you end up with a cubic equation which of course is a little more difficult to factor to determine the 3 roots which then give you 3 eigenvalues. Then its just a matter of substitution as Patrick showed you to get the eigenvectors.
Man you're an angel. This video helped a lot. Thank you so much.
My instructor must be a masochist. Had a 4x4 on the last exam.
Wow! Nice! Thanks! I read the slides of our class 3 times and understand nothing! This vid was a great help thank you!
As soon as you get to the row reduction, I'm lost. Dammit....
I sometimes cut class to watch these videos, soo worth it!
Have to do a 4x4 by hand.... fml
Thanks for spending the time to make these videos. They're make things a little more fun, but more importantly easier to understand and digest.
my instructor is a masochist...
more likely a sadist...masochism is self-inflicted pain
I was scrolling just to find a comment like this, lol
You're better than the doctor who teach us .
Thank you so much
1 hr before the exam and I'm not worried! Thanks Patrick
U deserve a nobel peace prize for your contributions to society fr
9 years later and still helpful. Thank you :)
I'm from nigeria and I have exams the questions they set are different from what they teach us and the man has made me understand what I'm learning
this has been very helpful, i was trying to watch a khan academy video but had lost me with it. this video really cleard things up for me :)
Thank you Mr. Patrick. in the classroom I can't understand then, That's why I had to suffer. Now I'm clear. Thank you again.
You make all lessons simple to understand 😎
Patrick, You are a life saver. Thank you Very Much for the Simplicity and the Outstanding Work.
Jesus Christ, you explained this in such a clear and precise manner that I managed to understand what my professor took over an hour to explain in under 15 minutes
i love the way you teach, I've been struggling in my Matrix Algebra course and your videos help me tremendously, thank you
I echo the comments below; great videos on this topic! I took LA 3 years ago and I didn't realize how much review I would get on determinants, row reduction, etc. Thanks!!
This is first of your videos I see, very well explained and easy to follow, thanks!
You actually teach properly, I did all this in my A-levels, and going into 2nd year of uni I'm brushing up on it. You go into the right amount of detail necessary and don't take what I'm predicting to be 3 lectures (150mins) to get there :P thanks
Thanks for this video. I was stuck at the part of how to determine the eigenvectors, and your video cleared it up for me. I really appreciate it! Keep the good work!
MAN...!! You saved my semester...!! Most accurate video to my course....THANK YOU SO MUCHHHHH..
Seriously you are amazing, Keep up with the fantastic work, it's making a difference.
Your explanation helped me tons! My textbook couldn’t even assist me, let alone my lecturer. Thank you 🙏
This is literally getting me into my next year of college,ut thank you
thank you so much! You explained the concepts in an easy-to-understand way, and I actually understand them now :)
This helped me understand what "diagonalizing" a 2x2 matrix for the schroedinger equation actually meant in my Solid State Physics class so THANK YOU!!!
happy to help :)
PatrickJMT and 3blue1brown - my favorite youtube channels
Nobody has ever teached this much perfect thanks a lot 😊
thank you sooo much, you saved my skin. God richly bless you brother!!!!
Very brief. Gonna ace my exams because of this. Thanks.
simple and very exaplanatory at the same time, thank you so much
Thank you! After 1 viewing of this and working out the example on paper, the concepts are so clear now.