In this video, I explained the meanings of eigenvalues and eigenvectors. I also did a step by step guide to computing them. The other eigenvector is [ 1, -2 ]
One of the most important concepts, encountered super frequently in so many branches of maths/stats/economics and even AI nowadays. Thank you for explaining Eigenvectors so nicely!
Mr Newton-you have just delivered an excellent exposition on a very important topic on Linear Algebra.Salute to you for your humble and yet professional delivery. Regards Dr.Sabapathy (Mathematician Singapore 🇸🇬)
As a student studying in German and having a maths exam next week, and therefore watch maths videos a lot here, I no joke did not understand the title for 2 minutes straight. Why Eigen but vectors instead of Vektoren? A nice surprise for me surely
Iam impressed by how effective and efficient the presentation of your online video lecture is ,am following you here in East Africa at South Sudan Juba
... Good day to you Newton, I need to add that " Eigen " is not only a German word, but also a Dutch word (lol), and now I'm continuing your presentation regarding LinAlg ... take care friend, Jan-W
@@utuberaj60 Good day to you sir, " Eigen " in Dutch means let's say " from me "' , "' my property "' , "' my possession " , e.g. ' mijn eigen huis ' means ' my own house ' or ' een eigen karakter hebben ' means ' having a character of his/her own ' ... I hope this made it a little clear to you?! ... take care, Jan-W
A German once said to me that only German speakers and Dutch (me) speakers can have a really true understanding of what an eigenvalue or an eigenvector is. And yes, I have spelled them correctly because in Dutch a noun is not spelled with an initial capital, in contrast to German.
Awesome. Your joy of teaching jumps from the screen, it's almost palpable. May I suggest a video class on the _geometrical_ interpretation of the eigenvalues and eigenvectors. I would love to see your take on this topic.
There's an easy way to calculate Eigen Characteristic Equation of a 2x2 Determinant The coefficient of x is the trace of the determinant (Sum of the Top Left and Bottom Right elements). And the constant term in the equation is the Determinant value of the Matrix.
So according to QuantumMechanics we live in a Determinant Universe? :-) I like your style of presentation. I do have a problem with determinant's however. To me they are just algebraic entities that are used to help work things out. But what are they? What is their reality in the Physical World? We use matrices to represent things, like Dirac did say, but what did the determinat of a matric mean in that conceptual bundle? I can agree that their use algebra is consistent and that adjuncts are only a little more blind numbingly dumb. I tend to see eigenvectors as a prefered direction and the eigenvalues are just their scalar, ie an attribute. What I can't see is the 'Physical' meaning of the determinant in all this. If a matrix is representative of a physical reality then its determinant must also be, but I haven't a clue as to what. You could accept that they are just algebraic flukes but that would be to doing what folk have been doing for the last 100 years, just calculating. I suppose I am looking for an intuative view of what a determinant is. It has bugged me for a life time, your presentation has rekinled my curiosity :-)
Great video Mr Newton. You explained this concept so fluently- something I could never assimilate from text books. I know that this idea is applied in Quantum Mechanics. May be next video you can give some actual applications of the EVs. Have a great day. You are wonderful 👍
Penso che questo professore sia uno dei migliori che abbia mai visto in tutta la mia carriera scolastica. Dopo tanti anni ho voluto iniziare di nuovo a studiare matematica e fisica perché dopo l'università non ho avuto occasione di applicarla nel mio lavoro. E' un vero piacere seguire le lezioni di questo signore!!!!!
Computing eigenvalues & eigenvectors shows-up ad nauseum in Math, Physics, Engineering, etc. A powerful application of Linear Algebra is in Differential Equations, where the concepts of eigenvalues, eigenvectors, orthogonality, inner product, etc. are used to construct solutions.
Question: in a matrix like 1, -1 1, 0 If I try to get the eigenvalues I end up with L^2 - L + 1 = 0 And now L must be complex. Do the eigenvalues and eigenvectors still exist as complex numbers, or do they not exist at all?
The very moment I see your smiling face, I feel happy! You are such an wonderful and passionate teacher sir!
One of the most important concepts, encountered super frequently in so many branches of maths/stats/economics and even AI nowadays. Thank you for explaining Eigenvectors so nicely!
If Lamda =3, then v=[-2
1] so, this is the eigenvector 2
And quantum mechanics! 🎇
Thank you so much! I'm currently studying this same topic! And your handwriting is amazing!
Mr Newton-you have just delivered an excellent exposition on a very important topic on Linear Algebra.Salute to you for your humble and yet professional delivery. Regards Dr.Sabapathy (Mathematician Singapore 🇸🇬)
Thank you! Glad you think so.
As a student studying in German and having a maths exam next week, and therefore watch maths videos a lot here, I no joke did not understand the title for 2 minutes straight. Why Eigen but vectors instead of Vektoren? A nice surprise for me surely
Thank you so much for the clear and methodical explanation.
Prime Newtons is our very own master teacher! Unser eigener Meister Lehrer! 🎉😊
Mate i'm studying for a test, yet your attitude is so fun, i'm actually starting to like linear algebra lol. Thank you man.
Sir your greatness is truly appreciated Thank you warmly from Iraq❤❤
This is spectacular. Thank you! Can you please go over repeated eigenvalues and their possible eigenvectors?
i love how excited you are
I wish you had been around 50 years ago. What a great explanation!
Iam impressed by how effective and efficient the presentation of your online video lecture is ,am following you here in East Africa at South Sudan Juba
This gentleman deserves more of my tuition money than my university
... Good day to you Newton, I need to add that " Eigen " is not only a German word, but also a Dutch word (lol), and now I'm continuing your presentation regarding LinAlg ... take care friend, Jan-W
Great. What does that mean in Dutch?
@@utuberaj60 Good day to you sir, " Eigen " in Dutch means let's say " from me "' , "' my property "' , "' my possession " , e.g. ' mijn eigen huis ' means ' my own house ' or ' een eigen karakter hebben ' means ' having a character of his/her own ' ... I hope this made it a little clear to you?! ... take care, Jan-W
You litteraly saved me for my final exam I love you
Congratulations!
[1,-2] is an eigenvector associated with the eigenvalue of 3.
Did you check it it satisfy AV=YV ?
No right?
@@bestvideo9158 buddy it did work plz check again!
very nice video! you actually explain the reasons for why we do what we do and it makes all the difference for learing!!
hi mr. newton im new to ur channel and ur vids are great and i have a doubt can u tell me how u find out the other eigenvector ?
such an awesome and passionate teacher, you make math fun and easy to understand, you even me laugh like, Yes I Get It! Thank you sir!
No unnecessary overexplaining or anything. You were amazing and calm explaining everything the whole time. Ty
It is good to see you in algebra video after the pause
Never stop learning..... Thank you so much
You are a life saver... U make me fall in love with algebra.. love from Sri Lanka...
A German once said to me that only German speakers and Dutch (me) speakers can have a really true understanding of what an eigenvalue or an eigenvector is. And yes, I have spelled them correctly because in Dutch a noun is not spelled with an initial capital, in contrast to German.
Inderdaad!
Just starting your mix on eigenvalue/eigenvectors and it's great. I've always struggled with these and your explanation of Av=lambdav is very helpful.
Woaw, your style, pauses and smile , everything is so good
Awesome. Your joy of teaching jumps from the screen, it's almost palpable. May I suggest a video class on the _geometrical_ interpretation of the eigenvalues and eigenvectors. I would love to see your take on this topic.
There's an easy way to calculate Eigen Characteristic Equation of a 2x2 Determinant
The coefficient of x is the trace of the determinant (Sum of the Top Left and Bottom Right elements).
And the constant term in the equation is the Determinant value of the Matrix.
BRO !!!! The first 2 min was enough to clear my ALL doughts PURE GOLD!!!!!!!!!!!
Ja, Deutschland ist überall.
May you guess what this languqge is😊
Thanks for teaching ❤️
This is very useful for me to understand the power system stability analysis and further study in my EE PhD. study
So according to QuantumMechanics we live in a Determinant Universe? :-) I like your style of presentation. I do have a problem with determinant's however. To me they are just algebraic entities that are used to help work things out. But what are they? What is their reality in the Physical World? We use matrices to represent things, like Dirac did say, but what did the determinat of a matric mean in that conceptual bundle? I can agree that their use algebra is consistent and that adjuncts are only a little more blind numbingly dumb. I tend to see eigenvectors as a prefered direction and the eigenvalues are just their scalar, ie an attribute. What I can't see is the 'Physical' meaning of the determinant in all this. If a matrix is representative of a physical reality then its determinant must also be, but I haven't a clue as to what. You could accept that they are just algebraic flukes but that would be to doing what folk have been doing for the last 100 years, just calculating. I suppose I am looking for an intuative view of what a determinant is. It has bugged me for a life time, your presentation has rekinled my curiosity :-)
Then we could conclude every vector of this form [2, -2] ... will also be an eigen vector corresponding to this matrix A? If not why?
Amazing videos, a full 10! Explained beautifully, clearly, best in youtube. Thanks
What a teaching style... Thank you very much. Highly appreciate ❤
Thank you for these videos! Your love for math is inspiring!
Great video Mr Newton.
You explained this concept so fluently- something I could never assimilate from text books. I know that this idea is applied in Quantum Mechanics.
May be next video you can give some actual applications of the EVs. Have a great day. You are wonderful 👍
That smile in ur face is the most beautiful beside your explanations, Thank you man ❤.
I don't usually comment but, you deserve a medal for this
Penso che questo professore sia uno dei migliori che abbia mai visto in tutta la mia carriera scolastica. Dopo tanti anni ho voluto iniziare di nuovo a studiare matematica e fisica perché dopo l'università non ho avuto occasione di applicarla nel mio lavoro. E' un vero piacere seguire le lezioni di questo signore!!!!!
The best explainer in the history for eigenvalues and eigenvectors.
Sir, please make a video on schrodinger's wave equation.
.....
The greatest lecture of all time ❤️❤️❤️❤️❤️❤️❤️❤️ you are amazing
I'm obsessed with how clean your board is ❤️
Thankyou, I love the way you teach, Its very unique
S0 de eigenvectors u will de coefficient as de answer
What if my X1 is > 1, eg 2,3 etc what will be my X2
Excellent review for me after so long ago.
Computing eigenvalues & eigenvectors shows-up ad nauseum in Math, Physics, Engineering, etc.
A powerful application of Linear Algebra is in Differential Equations, where the concepts of eigenvalues, eigenvectors, orthogonality, inner product, etc. are used to construct solutions.
I LOVE THIS DUDE'S ENTHUSIASM
Thnx boss uve really helped me
Mr. Newtons your video SAVED me. Thank you so much for the wonderful explanation sir.
You are over the bar. Excellent
Answer for V2 is 3 and -6
best teacher
Just Love Sir
I just wanna say thank you man
Thank you!
You're welcome!
How can i contact you sir
2 of mat {1 0
0 1}=2 x 1=2
when multiplying 2 and matrix it will become {2 0
0 2} then it will become 4
i just need answer
Eigen is a Dutch word. It means "own".
supper one 🥰
Thak you sir
The other eigenvector is (1,-2)
Wolfram|Alpha code:
eigenvectors | (1 | -1
2 | 4)
Great explanation, thanks so much
thank you sir for save my life!
nice
Wow
Very perfect explanation 😂👏👏👏 bravo!
Wea do you lecture so that I can apply there
Great explanation!
Glad you think so!
Hey bro, you're as cool as always!
This professor is really good....
You can record video about this
Prove that tr(A^{m}) = sum_{k=1}^{n}{λ_{k}^{m}}
in the near future
Is there a way to do that without talking about the Jordan canonical form? Or would I have to stick to diagonalizable matrices?
@@PrimeNewtons I thougth that there is easy explanation without Jordan form working for all matrices not only diagonalizable
@@holyshit922 Yeah. Maybe Shur form but there's a lot to explain. Maybe in the future.
doesn't the first eigenvector be not only [1,-1] but [any number, -any number] ?
also second eigenvalue has infinite number of solutions. Is it correct?
but of course. Eigenvector is kind of a misonmer since it is not unique. Think of it as Eigenspace that is the span of infinitely many eigenvectors...
can someone explain to my why the x1 = 1 in the eigen vector ? Btw great clip!
You just choose 1. You could choose any other number as long as it's nice for you. Just avoid 0 in this case so you don't get [0 0].
@@PrimeNewtons okk thank u
What a great teacher!
Man u are good
GREAT !!!!!!!!
You are awesome!
Question: in a matrix like
1, -1
1, 0
If I try to get the eigenvalues I end up with
L^2 - L + 1 = 0
And now L must be complex. Do the eigenvalues and eigenvectors still exist as complex numbers, or do they not exist at all?
Thank you sir
you are very much appreciated