Gershgorin Circle Theorem: Where The Eigenvalues Are!!

The Gershgorin Circle Theorem is a fascinating theorem that gives bounds in the complex plane on the locations of eigenvalues of a matrix. It allows for interesting proofs of the invertible of classes of matrices, and bounds on eigenvalues of classical matrices used in statistics!

#Gershgorin #LinearAlgebra #Eigenvalues

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[souravdey]

The perfect way to explain anything. First the barebones theorem, then the motivating example, then the proof, then the effects, then the extensions.

[MrMegaPega]

Even though i had already understood the concept and gotten what i searched for early into the video, i kept watching the entire thing, because you made me curious and excited about the possibilities. This very rarely happens. Thank you!

[Lakesaltwalker]

Like the fact that you give an example before explaining the theorem. It makes it easier to uderstand.

[uglycycle]

Your videos are really picking up steam! You shoot these all in one shot, like Birdman? You never stumble over any of your words!

[Idtelos]

Excellent video on this theorem. It helped a lot with a certain problem (24.4 from T.B for those who are curious) in a numerical linear algebra that I am taking. Thank you for posting it.

[jzjMacwolfz]

great explanation! thank you deeply, from china from an Ecuadorian struggling in Matrix!

[ayeshaanwarshaikh]

Thanks sir...Explained extremely well...You maintained the level of curiosity till the end

[Peter-bgku]

You just made an ostensibly difficult concept simple all thanks to your elegant explanation

[mohanveerubhotla]

Right to the point. Thank you so much. I found explanations which are way too complex but you explained it simply :)

[m.tajuddin]

Your videos are wonderful, you choose really interesting theorems. Please go on.

[Ibobfish]

I don’t realize the thm until I saw this
U save my finals
Thanks!

[Randomkloud]

Learning theorems in isolation just makes my mind spin. Thanks for the example at the end and the explanation for why this theorem is important, now it makes perfect sense.

I've noticed that all these math theorems are actually supposed to make our lives easier, too bad the way it's often taught in class makes it seem like a bunch of arbitrary rules! I suspect it's because it has become common sense for instructors and they can't fathom NOT understanding it

[Stelios]

It's nice that you made such a nice video on this non-standard-curriculum Linear Algebra theorem. As far as I know, it's useful for undergraduate students that participate in university level Math competitions. It would be wonderful whether you could make a video on how one could apply it to a competition Linear Algebra problem. I think that there may be some recent SEEMOUS or IMC problems that use this theorem, but I'm not sure... You could check them, if you'd like.

[zealshah]

thankyou for such an easy explanation.

[anoniem]

Djazak'Allahu khairan brother <3

[cyanide]

i have a question, for an eigenvalue, we got an inequality for the i(th) row, which proved that it belonged to the disc D(i), does that not mean that it belongs so every such disc D(i) and hence belong to the intersection of the n discs mentioned.

[zohrehabbasi]

Hi, is it applicable to columns as well?

[dajiazou]

Can you make a video about how Gershgorin Circle Theorem works with repeated eigenvalues?

[mohitseharawat]

I have n×n
real matrices A
and D
. D
is diagonal. Let's vi(A), λi(A)
be a couple of eigenvectors-eigenvalues of A
. What relationships there exists between vi(B), λi(B)
and vi(A), λi(A)
where B=DA
?

[ahiduzzamanahir]

Do you teach at a University? I'm transferring