Oxford Linear Algebra: Eigenvalues and Eigenvectors Explained

[@cll2598]

The only video on KZbin that explains both concepts in an intuitive way without compromising on the mathematical details

[@manfredvonrichtofen3863]

I am finally at a point at which I can use your videos as guide, not just as interesting videos about Math I dont understand :D

[@juliussoldan4016]

Just wrote my Linear Algebra 2 exam yesterday at UWaterloo. Admittedly, I had more of a love and hate relationship with these 2 courses, but near the end and looking back at them, I did really enjoy them. Seeing these videos and actually being able to understand what's going on just makes me realize how far I've come, and if I could go back in time I would definitely take them again.

[@TomRocksMaths]

Amazing!! Congrats :)

[@Abhisar_Gupta]

What a fantastic explanation. Thanks a lot.

[@owen7185]

Seriously it's great having someone who can teach math

[@lovisatroedsson5056]

Your voice is so nice to listen to…

[@jvdroid9074]

Man, that was the kind of video I was looking for, it was so good to watch. Thanks for you job!

[@rogeriojunior9459]

i wish i had learned it like that, but instead, the first time i saw it, was just proving hard theorems about existence of eigenvalues and eigenvectors, or orthonormal basis of eigenvectors or something like that, never had the time to actually play with the characteristic polynomial and find actual eigenvalues, great video

[@user-pp5lo5ky4i]

Here we go eigen.

[@TomRocksMaths]

I laughed

[@Kamyak]

Lol

[@duxxgd2733]

lmao

[@TomRocksMaths]

Check out ProPrep with a 30-day free trial to see how it can help you to improve your performance in STEM-based subjects: www.proprep.uk/info/TOM-Crawford

[@RC32Smiths01]

Always look forward to this quality information. Math with a fun and humble twist to it

[@koioioioi]

Although im still only in secondary school watching this is very interesting, so i will continue :D

[@rameshpanta8062]

Great intuitive explanation at the beginning. I was waiting for intuitive examples on its applications. Thank you !

[@rasainsbury]

In the 3×3 example, the eigenvector associated with eigenvalue -1 should be (1, 3, -3)'

[@nityambohare719]

I am waiting since ages of linear algebra's good lecture and my patience pay off thank you sir

[@pedrolironderobles3012]

As always, great explanations and very interesting content!!

[@owen7185]

Awesome Tom. I'll join Proprep as linear algebra I have this semester 👍👍

[@ACC861]

Would also be good to hear the geometrical notions of Eigen values and eigen vectors!!

[@TomRocksMaths]

But 3blue1brown is so much better for that!

[@ACC861]

@@TomRocksMaths Aha!! Love the shoutout to Grant!! I was hoping to get your thoughts on geometrical notions of EV's!! But regardless in recent times, I definitely watch 3Blue1Brown along with your videos to get a complete overview of the topics!! Recently, I have started watching Dr.Steve Brunton's (Associate Professor, University of Washington) channel too!! Afterall, the more insights that I get... the more I appreciate the lore behind the math!!

[@pepemosquera6005]

Great lecture! saw you at the duocon and decided to take a look to your channel, and this video was exactly what I needed for my algebra course, hoping to see diagonalization soon

[@tamasburik9971]

Wish I could've had you as my linear algebra prof

[@johnchristian5027]

Nice video, I love linear algebra!

[@umehmoses8118]

Love you Doctor, wish to meet you someday

[@RTD553]

Brilliant. But couldn't we just argue that the determinant of a transformation matrix represents the scale factor applied to the modulus of a vector? So if we want a result of zero when applied to a non-zero vector, we need a determinant of zero?

[@arthursteenkist2595]

Great lecture! 🙏🏻

[@tomasbruna3004]

Man, this is amazing.

[@darcash1738]

I was practicing elementary row ops for the 3x3 example, so I did r3 + r2/lambda. You end up getting an extraneous soln of 0. Btw how do you work backwards to get the A matrix from a given Eigenvalue and Eigenvector? Eg, lambda = 2, and (1, 0, 0) like the example. Or are these vectors sort of just for some characteristic of the matrix that is useful to us?

[@mnqobimsizi4328]

I WILL BE USING THIS METHOD TILL I DIE, IT EASY THAN DOING THE GAUSSIAN ELIMINATION

[@DistortedV12]

Does he talk about spectral values? SvD?

[@kiemanh1332]

at 8:38, i thought it supposed to be landa-5 at the first entry?

[@F89_]

ok there's one thing I'm slightly confused by. Where does the 6-landa come from? in my head that became 5 landa instead of 6 (I know this video came out one year ago but I'll shoot my shot.) I know this is a very simple thing to understand but I still don't really get it so yeah if anyone sees this and can explain it, it would be greatly appreciated 🙏

[@kanyamagaraabdallah8300]

merci frere je va retour sur ce video a bintot!

[@ihaveacreeplingdepression5708]

you are soooo goooooodd

[@KalyangoFredrick-k4h]

Where is the link bro?

[@unknown-fm5bm]

I have a question. z in every case to be any value ?

[@unruly_ronin]

This video has been the closest I've ever come to understanding this thing

[@juliusteo]

10:28 Why is the general vector a 2×1 and can it be a 2×n?

[@TomRocksMaths]

It would be n x 1 in the general case of a n x m matrix.

[@owen7185]

Would you state at the beginning that vector v is not zero? In an assessment situation?

[@rogerlie4176]

An eigenvector is by definition nonzero.

[@owen7185]

@@rogerlie4176 thank you

[@fabiangn8022]

gracias.😉👍🏾

[@InAMinMaths]

9:10 there’s a shortcut here where you can just put, where lambda = m, m^2 - (sum diagonal)m + detA which instantly gives the characteristic equation. I’m this case sum diagonal = 6, detA = 8. 10:06 better to complete the square.

[@guuguu7559]

a cool maths teacher doesnt exis- 😳

[@sidsiva3073]

You had written z=4z then went on to write z=0 . How ?

[@TomRocksMaths]

If you subtract z from both sides you get 3z=0 and so z=0

[@ummerfarooq5383]

That 30 second explanation.

[@souravchakraborty6766]

🙌🙌🙌🙌

[@chanceneck8072]

Own values? 😅🤔🤷‍♂️

[@davidmurphy563]

Ok, the linear algebra is fine but the factorisation is basically witchcraft. I'll ask my son to teach me.

[@donegal79]

unfortunately, this simply goes through the simple mechanics of determining values - zero explanation, insight, into what these represent. Frankly, could have gotten a smart 14 year old to do this video. You need to up your game mate, stop appealing to middle of the road engineering students.

[@irtazakhan2243]

Sod off