6: Eigenvalues: Why det(A-λI) = 0 - Learning Linear Algebra

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Күн бұрын

Full Learning Linear Algebra playlist: • Learning Linear Algebra Finding eigenvectors and eigenvalues. Why do we set the determinant of A-λI to zero? The explanation's right here!
Video on determinants: • 5: Determinants, Inver...
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Пікірлер: 29

@kev7355 4 жыл бұрын

Holy cow. I finally understand this after 20 years. Did this in college back then but never quite understood why det=0.

@domination2720 4 ай бұрын

best by far on this topic

@adityaapoorva2370 Жыл бұрын

Thank you so much, the explanation was really simple I understood it in one go.

@SnehilRayal Жыл бұрын

Thank you for such lucid explanation 🙂

@sudipdas4596 4 жыл бұрын

Seriouly, you have tremendous teaching skills. Soved many problems, completed GIlbert strang's videos, had many doubts, this video ironed out the doubts. Love from india

@RoodJood Жыл бұрын

Gilbert Strang and Dr Grinfeld are on another level

@jaidonlybbert8853 4 жыл бұрын

Great video. Concise, informative, and well edited.

@Junyan-ft5vn 2 ай бұрын

Thank you!!!

@jarednair2516 3 жыл бұрын

This is great stuff, thank you!

@franks8249 2 жыл бұрын

Cool video! Clear explainations.

@springvibes5344 9 ай бұрын

Thank you

@HAL-oj4jb 5 жыл бұрын

Very nice explanation! Is there some easy way to understand why the determinant being equal to zero is a sufficient criterion for an eigenvalue? I always wondered why this is enough to find them (besides checking explicitly).

@MuPrimeMath 5 жыл бұрын

In the video linked in the description, I talked about why the determinant being zero means that the matrix has no inverse. If the matrix M has no inverse, then Mv=0 has multiple solutions, which is what we need for an eigenvector to exist.

@Sagar-fd5ls 3 жыл бұрын

Great Video!

@mohamedmaher9747 4 жыл бұрын

Thanks alot.. Simple explanation 👌

@goshikaamarnath2868 4 жыл бұрын

Nice explanation

@SSNewberry 10 ай бұрын

Gilbert Strang would be proud.

@MoonLight-sw6pc 5 жыл бұрын

Nice! Keep going .....

@hcchang4392 3 жыл бұрын

Thank you !

@mansipatel8538 5 күн бұрын

I love you

@justinchow1644 Жыл бұрын

only you explained why det=0 is necessary. thanks!

@freudboyxd3430 2 жыл бұрын

How can i get a t shirt like yours? O.O

@MuPrimeMath 2 жыл бұрын

Tie dye!

@NormanWasHere452 2 жыл бұрын

It’s not even that complex to understand why, for some reason it’s just not really explained in textbooks and definitely not by my lecturer lol

@lilmaxez 2 жыл бұрын

Let A,B ∈ Mn. If rank(A) < n/2 and rank(B) < n/2, show that  det(A + λB) = 0 for some complex number λ.

@matthewjames7513 2 жыл бұрын

Great video. But I don't think this is a thorough proof because at 3:16 you assume that that other solutions that aren't v= 0 exist to motivate why the inverse can't exist. Once you know other solutions that aren't v=0 exist, then you can use your logic to show that det(A) =0. Btw It's ofcourse true that other non trivial solutions exist, but you need to prove it first for your logic to work.

@MuPrimeMath 2 жыл бұрын

This video does not prove the existence of eigenvectors; it proves some properties that eigenvectors must satisfy if they exist. We suppose that v is a nonzero eigenvector and use that derive the matrix conditions.

@matthewjames7513 2 жыл бұрын

@@MuPrimeMath Hey thanks for the reply! And thanks again for all your videos. I've been watching a lot of them and I really like your teaching style :) I agree with you that "This video does not prove the existence of eigenvectors; it proves some properties that eigenvectors must satisfy if they exist". But I really think you need to prove non zero solutions exist before, or prove that the eigenvector solution satisfies Ax = λx afterwards. Otherwise there is no benefit. Here's a simple 1D example using your logic to illustrate my point: Find all integer solutions to the equation x/a = 1 where 0

@casinarro 3 ай бұрын

@@matthewjames7513thanks for the example, now I get your point.