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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[@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!

[@ProfOmarMath]

Thanks Jan! Would love to hear about other curiosities you have that I can share about!

[@Lakesaltwalker]

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

[@ProfOmarMath]

Definitely. It motivates a reason to care.

[@shantipriya2905]

@@ProfOmarMath Yes example is more important to explain anything

[@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!

[@ProfOmarMath]

Thanks Josh! Birdman or 1917, who knows 😂
Having fun though. If there's anything you or your students want to see lemme know for sure!

[@Peter-bg1ku]

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

[@ProfOmarMath]

Thanks Peter, I appreciate that!

[@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.

[@ProfOmarMath]

Hi Idtelos. No problem! It's an interesting theorem, short with nice consequences. Curious, what other related theorems come about?

[@Idtelos]

@@ProfOmarMath Ovals of Cassini come to mind.

[@ayeshaanwarshaikh2180]

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

[@ProfOmarMath]

Thanks Ayesha!

[@jzjMacwolfz]

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

[@ProfOmarMath]

Thanks!

[@m.tajuddin]

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

[@ProfOmarMath]

Thanks Muhammad! And yes, more to come quite soon 😁

[@ProfOmarMath]

Just a quick question: is there a theorem you are particularly interested in?

[@mohanveerubhotla8277]

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

[@ProfOmarMath]

Thanks Mohan, happy you enjoyed!

[@kenthedawg6383]

Great video! Really neat theorem!

[@Ibobfish]

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

[@ProfOmarMath]

Awesome!

[@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

[@tarakmehtakaultacashma9863]

You're doing great 👍 👏

[@ketz108932]

Excellent Explanation

[@ProfOmarMath]

Thanks ketz!

[@1991newton1]

Thank you.. it was good to me

[@zealshah9]

thankyou for such an easy explanation.

[@ProfOmarMath]

Definitely!

[@Stelios2711]

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.

[@ProfOmarMath]

Stelios, thanks for these. I'll take a look for sure. The IMC has some interesting ideas. I think I'll be making videos on sharing a technique followed by how it is implemented, with many many examples. Makes things more nice and compact.

[@anoniem012]

Djazak'Allahu khairan brother

[@aboodahmad8236]

Jazak°

[@anoniem012]

@@aboodahmad8236 Why are you trying to correct Latin alphabet grammar? Hahahha, we all know that there are multiple ways to write it down since it is from Arabic, and every country has few things as different pronounciation of Latin letters.

[@cyanide7833]

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.

[@omargaber3122]

Great. Thank you

[@ProfOmarMath]

Thanks for watching!

[@stergios_tournavitis]

wonderfull video! Congratulations!

[@ProfOmarMath]

Thanks Stergios!

[@saltycoins8835]

thanks for the video!

[@ProfOmarMath]

Thank you!

[@diprajkadlag]

thank you very much for the video..

[@ProfOmarMath]

Definitely!

[@no-qm1kn]

Genius.

[@cvismenu]

Thank you

[@mohitseharawat2551]

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
?

[@Anilkumar-dv8ib]

This is good one 👍

[@ProfOmarMath]

Thanks Anil

[@dajiazou6592]

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

[@ProfOmarMath]

Hi Dajia. What did you have in mind in particular regarding it?

[@dajiazou6592]

Oh, thank you for reminding me.

[@ahiduzzamanahir1338]

Do you teach at a University? I'm transferring

[@shohamsen8986]

Nice theorem.

[@ProfOmarMath]

So cool huh?

[@shohamsen8986]

@@ProfOmarMath I mean there is a distinct possibility of looking at a special matrix and just claiming that it's non-invertible. I can imagine the shock of the people around me when I do so. :P

[@achrafben7203]

Hi. Have you the proof of Hille-Yosida theorem ?
1001 thanks from Algeria 🇩🇿

[@ProfOmarMath]

I haven’t! Tell me about it.

[@achrafben7203]

@@ProfOmarMath
OKAY. THANK YOU.👍

[@omargaber3122]

Where did you disappeared?

[@aashsyed1277]

perfect square likes AND also perfect square dislikes

[@ramosluis4511]

could you speak spanish? :c i´m UNMSM

[@ProfOmarMath]

I wish I knew Spanish 😞

[@ramosluis4511]

@@ProfOmarMath don't worry, you're Wonderful.

[@ProfOmarMath]

@@ramosluis4511 Flattering 🤗