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 ]
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
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 🇸🇬)
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!!!!!
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.
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 👍
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
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.
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.
... 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
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 :-)
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?
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
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! 🎇
You litteraly saved me for my final exam I love you
Congratulations!
Prime Newtons is our very own master teacher! Unser eigener Meister Lehrer! 🎉😊
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.
I wish you had been around 50 years ago. What a great explanation!
Thank you so much! I'm currently studying this same topic! And your handwriting is amazing!
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!!!!!
Sir your greatness is truly appreciated Thank you warmly from Iraq❤❤
It is good to see you in algebra video after the pause
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.
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.
Mr. Newtons your video SAVED me. Thank you so much for the wonderful explanation sir.
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 👍
Amazing videos, a full 10! Explained beautifully, clearly, best in youtube. Thanks
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 is spectacular. Thank you! Can you please go over repeated eigenvalues and their possible eigenvectors?
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 ?
You are over the bar. Excellent
This professor is really good....
best teacher
Just Love Sir
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.
[1,-2] is an eigenvector associated with the eigenvalue of 3.
Did you check it it satisfy AV=YV ?
No right?
Great explanation, thanks so much
Very perfect explanation 😂👏👏👏 bravo!
You are awesome!
Sir, please make a video on schrodinger's wave equation.
.....
Great explanation!
Glad you think so!
Hey bro, you're as cool as always!
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!
... 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
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 :-)
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?
Man u are good
GREAT !!!!!!!!
Wea do you lecture so that I can apply there
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
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
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...
S0 de eigenvectors u will de coefficient as de answer
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.
Ja, Deutschland ist überall.
May you guess what this languqge is😊
The other eigenvector is (1,-2)
Wolfram|Alpha code:
eigenvectors | (1 | -1
2 | 4)
Eigen is a Dutch word. It means "own".