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!

@deckeresq

5 жыл бұрын

Please definitely post a 3x3 example! This is super helpful.

@zeeshanchaudhry3324

4 жыл бұрын

Can you generalize discuss the implications of the cases where the eigenvalues come out as imaginary?

@orange399

4 жыл бұрын

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

@apollosleaf731

4 жыл бұрын

Do we have to follow all these steps or is there a faster way to go about it?

@bhumikasrineel6799

4 жыл бұрын

Please take an example of solving 3×3 matrix too

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!

@patrickjmt

7 жыл бұрын

+The Visionary I'm sure I've helped a few here and there :)

@bigbubbadave7370

7 жыл бұрын

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.

@Ghost572

7 жыл бұрын

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.

@andrebayan

7 жыл бұрын

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.

@balkdermins1528

7 жыл бұрын

hey where are you studying Mechanical Engineering > .. Im studying it At the University of Guyana

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

@KH-ft4ut

6 жыл бұрын

Just did the same with an exam coming up in 2 weeks. Why do we do these things to our self?!?

@chukwumannadi706

6 жыл бұрын

LMAO!.

@Sam-wt1cx

5 жыл бұрын

@@KH-ft4ut Exactly.. My exam is in just after 2 weeks and I ve started to look at things just now

@KH-ft4ut

5 жыл бұрын

@@Sam-wt1cx Good luck mate, I passed my exam. But I still have no idea what Eigenvalues or eigenvectors are actually useful for.

@jgc9199

5 жыл бұрын

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.

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.

@adamc5478

8 жыл бұрын

+Allegro Crab introductory ?Linear algebra?

@Macca-95

8 жыл бұрын

+Allegro Crab It's currently 1:15am here, my exam is 9am. I can relate :P

@Poodz_

8 жыл бұрын

HaydenMcM1 you're australian too? good luck m8.

@Macca-95

8 жыл бұрын

***** Yep, thanks mate :)

@edacordon126

8 жыл бұрын

its already 2016 but I can relate to what you said. its 2am and I have my exams later at 9am. 😂😂

fools cant even explain this in an hour. patrickjmt is a beast.

@fairax

8 жыл бұрын

When they explain this stuff in an hour they just rush through it and don't explain anything, Patrick is a life saver

@ReWolWerKillZ

8 жыл бұрын

Eric Da Silva Uni profs are usless bro

@ProductionBandit

8 жыл бұрын

i guess thats why there's that saying "those who can, do; those who can't, teach"

@ghostf6321

7 жыл бұрын

Yea seriously if it weren't for patrickjmt and other KZreaders I would have no idea wtf is going on in my diff eq class.

@patrickmoloney672

7 жыл бұрын

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 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

@hxqing

2 жыл бұрын

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.

@sdlion7287

2 жыл бұрын

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.

let me just say... you are single handedly saving me this semester.

@jianeecarrasco9106

3 жыл бұрын

Literally !

You sir, are a God amongst men. Thank you for these videos, you legend.

@patrickjmt

9 жыл бұрын

+Flambe nah, just a normal guy trying to help in the best way i know how!

@kentrelljackson

8 жыл бұрын

+patrickJMT JOHN 8:32 :) #lifeabove

@reiantaank3314

8 жыл бұрын

+Flambe I don't think it's right comparing him to god. I mean he's good... but he's no Patrick.

@superchargedAMG

7 жыл бұрын

definitely a god among men

@rgseven6557

7 жыл бұрын

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 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.

@patrickjmt

10 жыл бұрын

i am already rewarded by feeling appreciated in this world as your comment does for me ;)

@user-lk3pq3ne3f

6 жыл бұрын

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

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 :)

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!

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!

In that case, my instructor is a masochist

@TheZwhyX

8 жыл бұрын

+HaydenHatTrick same

@cjlooklin1914

8 жыл бұрын

Lol, I think you mean sadist, my Eigen value were 5.372 and -.372.......

@SuperLuckyKill

8 жыл бұрын

+Cj Looklin Tell your professor to screw off. I feel so sorry for you

@Recon13x

7 жыл бұрын

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

@datascientist3663

4 жыл бұрын

Oh noooooooooooooooooooooooooooo

doing maths along listening to your videos is blissful!

@patrickjmt

9 жыл бұрын

Ha, glad you feel that way!

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.

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!

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.

Thanks for the video, sorry, can You please explain how you came to 3R1+R2 >R2 when determining the eigenvectors? Thank you in advance

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.

You sir, are a lifesaver.. Finally taught in a way that I can understand fully. Great job man, and thanks.

Is there a word more than thank you.ahh I appreciate this. no there must be something better. You are a complete University.

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?

@plpI1

2 жыл бұрын

yes any number you can since it just a scalar. For simplicity just pick number 1.

You're a good soul! I have benefited from many of your videos. Thanks for the help!

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!

I cannot express how grateful I am for linear algebra libraries, saving me from having to do any of this

@estebanlopez1701

4 жыл бұрын

Jajaja I couldn't agree more. It's pitiful how many teachers are reluctant to integrating technology to subjects like this

my teacher teaches a same question by very complicated method but your method is so understandable thnks sir :-)

I've seen two video's about eigenvalues and eigenvectors and am amazed. Amazingly clear instructions.

thank you so much! You explained the concepts in an easy-to-understand way, and I actually understand them now :)

I wish my physics lecturers at university had been like you.

greatest youtuber!

Amazing, I learn here in 5 minutes what didn't learn with my teacher in 2 hours. Keep up the good work Patrick.

You have literally helped me 4.0 all 3 calc classes, my proofs class, and now linear algebra. Thank you!

You are the best at explaining! I love your videos

@patrickjmt

9 жыл бұрын

Thanks!

@XXgamemaster

8 жыл бұрын

+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?

@Fabizy

8 жыл бұрын

+JC Tutoring it's the same if you make the second row of the matrix have all zeros, you still have same result

@syd_jzx100

7 жыл бұрын

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.

Can you please put all linear algebra videos in one playlist ? that would be wonderfull but thank you Patrick!

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!

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!!

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?

@chockesondicks7505

6 жыл бұрын

Yeah, like you can also use the letter A for example X2= A and X1=3A

@seansethi196

2 жыл бұрын

I have the exact same question, choosing 1 seemed arbitrary but I do not understand why it was chosen.

@moatef1886

2 жыл бұрын

@@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.

@seansethi196

2 жыл бұрын

@@moatef1886 appreciate the reply, thank you!

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?

I've never commented on a KZread 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.

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

in 7:10 you wrote 3R1+R2→R2 How do you pick exact these values ?? for row one and two

@matf6661

5 жыл бұрын

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.

@gamersden30

5 жыл бұрын

Thank you from Australia

@HariPrabhuJAP

5 жыл бұрын

Welcome from india

Why we let x2 = 1 I don't understand, please help

@bobbutts524

9 жыл бұрын

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

@bobbutts524

9 жыл бұрын

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.

@Khalil9497

9 жыл бұрын

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

@andyroutine132

9 жыл бұрын

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

@skylarkenneth2407

5 жыл бұрын

​@@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 love the way you teach, I've been struggling in my Matrix Algebra course and your videos help me tremendously, 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

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

2 жыл бұрын

yes i want to know about this too

@sauceandalouse2624

2 жыл бұрын

@@shirashira8871 I'm in the same position hahah I want to know too

@sauceandalouse2624

2 жыл бұрын

@@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."

@shirashira8871

2 жыл бұрын

@@sauceandalouse2624 Thank you for your explanation:)

Do you have any video on diagonalization of matrices ? Thanks for the helg witn Eigenvalues-vectors :)

@aman7697

5 жыл бұрын

I love you baby 😊😍😘😚😗😙

Patrick, You are a life saver. Thank you Very Much for the Simplicity and the Outstanding Work.

Without doubt the best video on the web for eigenvectors and eigenvalues. Thanks a lot this masterpiece.

I can pinpoint the exact moment when you lost me :D 7:00

@peterlee5726

4 жыл бұрын

Hey it's been 3 years but yeah.... WTF is row reduction?

@ducksoop.x

4 жыл бұрын

@@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.

@Josh-zk7pf

4 жыл бұрын

Peter Lee I know your comment is old, but KZread for his video called “gauss-Jordan elimination” that’s what row reduction is

@NayAPakistanJobs

4 жыл бұрын

but why we need row reduction here

@BoburMamadzhanov

3 жыл бұрын

Could anybody explain it to me please?

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 :(

@supahotfire8886

3 жыл бұрын

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!

@AceofDlamonds

3 жыл бұрын

@@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.

@litjew6669

11 ай бұрын

are you an engineer now lol@@AceofDlamonds

@AceofDlamonds

11 ай бұрын

@@litjew6669 Hehe...i'll just say I wish I could rewind time and study computer science instead 😂

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.

Great video, doing this in matlab and it's just great to know what the maths behind it is rather than just putting numbers in and getting numbers back, thanks a lot!

That sharpie though. So squeaky. The video is fantastic though.

@MrJaros

6 жыл бұрын

Kind of a comforting sound tbh

You think you can do a 3x3 matrix?

@rwh777

9 жыл бұрын

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.

You explain everything so well, I finally understand how to find the eigenvectors!! THANK YOU!

Thank you! After 1 viewing of this and working out the example on paper, the concepts are so clear now.

Doesnt that mean there are infinite eigenvectors?

@staceyburchette3276

8 жыл бұрын

Yes, once you find an eigenvector, any scalar multiple of that vector will also be an eigenvector.

2 minutes in and im already understanding more from this than my slides from my uni website, god bless you

clear, concise without missing a step, great help, thanks

7:10 where did the 3 come from? 3xR1 + R2 = R2 ??? !!!

@samanthaseetaram1516

4 жыл бұрын

Can someone answer this plz????

@yoga5631

4 жыл бұрын

It's a variable, i think he is using the gauss Jordan formula

@hpyakurel

4 жыл бұрын

he is trying to reduce it in echelon form.

Have to do a 4x4 by hand.... fml

i must admit that left handed people are always somehow gifted and special. thanks for helping man !!

i'm doing research on Principal Component Analysis, and your guide is so useful. thanks .. it's very easy to understand.

As soon as you get to the row reduction, I'm lost. Dammit....

“Unless the instructor is a real masochist” thanks for accurately describing my math teachers

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!!

I´m so greatful for your explanations! If it weren´t for them I could never fix this course.

My instructor must be a masochist. Had a 4x4 on the last exam.

my instructor is a masochist...

@MrJaros

6 жыл бұрын

more likely a sadist...masochism is self-inflicted pain

@floydnelson92

6 жыл бұрын

I was scrolling just to find a comment like this, lol

Thank you sooo much for teaching in a wonderful way and turning complicated things into easy things...👍👍👍

Thank you for providing such a good example AND showing a good method to check. This helped a lot, thank you!

SO GOOD! Without unncesseary explanations, on point, ty!

I can always rely on you! Thank you so much!

This is first of your videos I see, very well explained and easy to follow, thanks!

Seriously you are amazing, Keep up with the fantastic work, it's making a difference.

March 2019 and it is still very useful video, I appreciate your teaching style!

thank you sir for the amazing video it's really helpful , i was reading my control assignment and you kind of saved me :) thank you so much

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 🙌

very helpful patrick, thank you so much for your hard work and dedication

I just wanna say thank you for all the great help .. you are really doing something useful for all the students . I wish someday to do something as good

What if for example there is no x value for the basis in finding the P? like for example you find first equation: x1+x3=0 then 2nd equation: -x1=0 as you can see there is no x2 value. So would I put the x2 value as zero? or try doing the matrix again?

simple and very exaplanatory at the same time, thank you so much

Thanx a lot! Great video! Helped me a lot for my final.

MAN...!! You saved my semester...!! Most accurate video to my course....THANK YOU SO MUCHHHHH..

at 8:00, are you allowed to make xsub(2) any value you want or is there a specific reason making it = 2?

This is literally getting me into my next year of college,ut thank you

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.

@stanleychan2099

9 жыл бұрын

May I ask for an application example for Eigenvectors and Eigenvalues such as Page Rank algorithm?

Patrick you are a good tutor such that your naked all concepts to my sight. keep it up. Thanks

Such a beautifully lucid explanation. Thanks a lot!

awesome explanation *_* each step was pretty clear

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.

You are the main reason why I'm passing my Math and calculus courses...Respect Math Boss

Wow I read lots of books on this topic and now I understand it. You are the best!

I sometimes cut class to watch these videos, soo worth it!

You're better than the doctor who teach us . Thank you so much

Thank you Patrick! This video really helped me with Eigens...!

great set of instructions!!!!! thanks a lot for these videos

9 years later and still helpful. Thank you :)

You make all lessons simple to understand 😎