Eigenvalues and Eigenvectors

[@sudiptoatutube]

The very moment I see your smiling face, I feel happy! You are such an wonderful and passionate teacher sir!

[@saba6601]

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 🇸🇬)

[@PrimeNewtons]

Thank you! Glad you think so.

[@fathertedczynski]

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!

[@AliBarisa]

If Lamda =3, then v=[-2 1] so, this is the eigenvector 2

[@dirklutz2818]

And quantum mechanics! 🎇

[@punditgi]

Prime Newtons is our very own master teacher! Unser eigener Meister Lehrer! 🎉😊

[@SimoneMarion]

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!!!!!

[@wad2k]

some people are born to teach... sir you are one of these people! i did not want to study this topic because it seemed complex and uninteresting - however, after watching this video you have made it both entertaining and simple to grasp. thank you very much.

[@PrimeNewtons]

Wow, thanks

[@ChillyGFX]

W wad

[@wad2k]

@@ChillyGFX gotta show some love 💯.

[@yashgupta4099]

BRO !!!! The first 2 min was enough to clear my ALL doughts PURE GOLD!!!!!!!!!!!

[@bobthebuilder2789]

No unnecessary overexplaining or anything. You were amazing and calm explaining everything the whole time. Ty

[@chuckblevins-227]

I wish you had been around 50 years ago. What a great explanation!

[@mallika9363]

Thank you so much! I'm currently studying this same topic! And your handwriting is amazing!

[@موسىعمادبهاءالدين]

Sir your greatness is truly appreciated Thank you warmly from Iraq❤❤

[@alexanderst.7993]

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.

[@maelysbourry1041]

You litteraly saved me for my final exam I love you

[@PrimeNewtons]

Congratulations!

[@thisisanexcellenthandle]

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

[@imrannouaji2110]

Man that's just pretty smooth to be understood, now i learned about eigen things with a weak mathematics background, thank you sir!

[@hqs9585]

Amazing videos, a full 10! Explained beautifully, clearly, best in youtube. Thanks

[@eduaid777]

You are a life saver... U make me fall in love with algebra.. love from Sri Lanka...

[@engmajeed98]

The best explainer in the history for eigenvalues and eigenvectors.

[@muhammadusman75231]

Woaw, your style, pauses and smile , everything is so good

[@greatgreatleo]

very nice video! you actually explain the reasons for why we do what we do and it makes all the difference for learing!!

[@theohewey7243]

I love this guy. So easy to understand and great energy.

[@mikefochtman7164]

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.

[@AkeenAker]

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

[@KPl8184]

Thank you so much I watched so many videos and this is the only one that made sense

[@alicianieto2822]

This gentleman deserves more of my tuition money than my university

[@shahmohammadyasin5745]

Idk about eigenvectors or eigenvalues, but you sir are the real life saver ❤

[@sithumakash5756]

What a teaching style... Thank you very much. Highly appreciate ❤

[@zikraabdusemed]

The most amazing Video I have ever watched. you make mathematics' easy and understandable. I wish all teachers were like you.

[@deekshamohanty]

Mr. Newtons your video SAVED me. Thank you so much for the wonderful explanation sir.

[@diclekucukkaraca3689]

I don't usually comment but, you deserve a medal for this

[@CEESAYMADI-c1j]

Thanks a lot, Mr. Newtons. Your explanations are just amazing and easy to comprehend.

[@omk7x]

That smile in ur face is the most beautiful beside your explanations, Thank you man ❤.

[@michaelrodriguez6791]

Thank you for these videos! Your love for math is inspiring!

[@jackdeago3639]

Never stop learning..... Thank you so much

[@SunandMoon7-7]

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!

[@MatiYouTube-u4l]

you are prefect teacher❤ I never seen any one like you, you best of best for ever, from Ethiopia

[@itsfrankie9570]

i love how excited you are

[@cidapp7621]

Thank you so much for sharing your competencies in Mathematics. More power!

[@faustobarbuto]

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.

[@mathewshamanjile914]

The greatest lecture of all time ❤️❤️❤️❤️❤️❤️❤️❤️ you are amazing

[@christianjerry896]

omg....u are literally a life saver sir

[@holyshit922]

It is good to see you in algebra video after the pause

[@0ShadowMonarch]

I LOVE THIS DUDE'S ENTHUSIASM

[@Aadhyaxx]

Hats off to you sir!! u explained the concept so beautifully, supporting you here from India!

[@zaccai3927]

I'm obsessed with how clean your board is ❤️

[@wiloberlies9598]

Absolutely wonderful lecture, so clearly explained. Thank you.

[@georgetallah6568]

You are over the bar. Excellent

[@utuberaj60]

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 👍

[@AlexanderDaniluc]

Amazing lecture, you have a great teaching style. Very positive, engaging and helped me learn. Earned a sub and like!

[@cristiano_07-l5m]

The best gift of 2025 that i found a legend ❤

[@Avyskier]

This is spectacular. Thank you! Can you please go over repeated eigenvalues and their possible eigenvectors?

[@prantomollah4899]

best teacher Just Love Sir

[@kdhd100]

This professor is really good....

[@JohnsonIdris112]

Now I feel motivated to study linear algebra, thank you Sir.

[@johannadsouza439]

Thankyou, I love the way you teach, Its very unique

[@EasternDresses]

Thanks so much - Subscribed to the channel because its very precise and relevant content.

[@hrishikeshkulkarni8955]

Thank you so much for the clear and methodical explanation.

[@nozomikwok4343]

Thanks for teaching ❤️ This is very useful for me to understand the power system stability analysis and further study in my EE PhD. study

[@Sleepy_hats2024]

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 ?

[@valor36az]

What a great teacher!

[@jan-willemreens9010]

... 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]

Great. What does that mean in Dutch?

[@jan-willemreens9010]

@@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

[@tikarambhattarai2690]

supper one 🥰

[@ANANTHARAMAKRISHNANSUBRAMANIAN]

What a explanation. Lots of luv:)

[@RachitAryanAsthana]

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.

[@jamesmunroe6558]

Great explanation!

[@PrimeNewtons]

Glad you think so!

[@frankteunissen6118]

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.

[@dirklutz2818]

Inderdaad!

[@eiko-ur1ko]

Thank you for ur lecture and please upload for Multiple Eigenvalues and Eigenspace also

[@unzamathematicstutormwanaumo]

Very perfect explanation 😂👏👏👏 bravo!

[@douglasstrother6584]

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.

[@nakyejwesarah4040]

Thnx boss uve really helped me

[@jacobgoldman5780]

[1,-2] is an eigenvector associated with the eigenvalue of 3.

[@bestvideo9158]

Did you check it it satisfy AV=YV ? No right?

[@_foley_6371]

@@bestvideo9158 buddy it did work plz check again!

[@tonui6114]

Great explanation, thanks so much

[@KiteFives]

I just wanna say thank you man

[@0day450]

thank you sir for save my life!

[@abhinavmaurya_]

Love' from India ❤

[@RahulSingh-dr1dl]

Sir, please make a video on schrodinger's wave equation. .....

[@rabiumuhammed3496]

You are awesome!

[@YihunAyitenew]

thanks for you mis,

[@mohammadesmailnazari8516]

Greetings sir, thank you for your informative video. I have a question regarding the eigen vectors: how does one determine the eigen vector from the eigen value if the matrix is of 3x3 or nxn dimensions? Also, Is there a simpler way to do it, because this process for the nxn matrixes in the course of modern control, can be quite time consuming!

[@yuvarajum2594]

Fantastic

[@rajgopalpaithara1388]

Thank you Sir.

[@thegreatest2222]

Great Vid🎉, but can someone explain to me how at 8:22 he got -5 lambda using distribution? I understand how he got all of the other numbers

[@WrongDescription]

Thank you!

[@PrimeNewtons]

You're welcome!

[@mathewshamanjile914]

How can i contact you sir

[@libsxdium]

Hey bro, you're as cool as always!

[@aryatuhwerajimmy3892]

Wea do you lecture so that I can apply there

[@alphalunamare]

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 :-)

[@williamsojah8402]

Man u are good

[@cupckae1]

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?

[@anthonycroft7538]

So when you say that each eigenvalue has its own eigenvector what you mean is that the the x,y values of the corresponding eigenvectors have a proportion between them which you have determined through the maths you very clearly illustrate. But there is not a single vector that satfisfies the equation, there are multiple, as long as you keep the proportionality between x1 and x2. That may be clear to everyone else but I had to convince myself with some examples that the answer vector is in fact a set of vectors. [NB: This happens because eigenvectors span a one-dimensional subspace (a line through the origin) in the direction of the eigenvector. Any vector along this line is a valid eigenvector.] You might want to show what this all means geometrically because I think that gives a more intuitive meaning beyond the pure maths. It would also be useful to provide an example of where this is useful in solving a real life problem such as in ML.

[@fikrulihsanarifin1301]

GREAT !!!!!!!!

[@priyanshurao6212]

Sir, for a particular value of x1 we have our x2 ,so u trying to say that there are infinite eigenvectors for a given eigenvalue. Cause if we chose any other number instead of 1 for x1 so we end up with another value of x2.

[@Cycrypt01]

Thak you sir

[@ChideraOgbonna]

What is V2

[@amoscasey6114]

What if my X1 is > 1, eg 2,3 etc what will be my X2

[@AhmedHassan-gj2vc]

nice

[@mints7649]

i love you prime newtons

[@PlayngThai2]

A square matrix A is invertible if and only if det A ≠ 0.

[@jbasanth4896]

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

[@kuber2455]

doesn't the first eigenvector be not only [1,-1] but [any number, -any number] ?

[@kuber2455]

also second eigenvalue has infinite number of solutions. Is it correct?

[@Yougottacryforthis]

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...