Complex eigenvectors

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Күн бұрын

Пікірлер: 29

@kragiharp 10 ай бұрын

Thanks so much for reviewing all the stuff I have forgotten over the years! I haven't needed all this since my school and college days, but it was so much fun back then. ❤️🙏

@kevinbush4300 10 ай бұрын

I agree... I loved Linear Algebra when I was an undergrad. Not had much use for it since I went to work in a casino.

@stigastondogg730 10 ай бұрын

Same here! Still have no idea what eigenvectors are for in a practical sense haha

@kragiharp 10 ай бұрын

@@stigastondogg730 I needed eigenvectors in linear algebra for circuit analysis back in college in a sophomore or junior course. So I guess it is used for developing chip technology today. But I switched my aim for my degree and haven't finish this subject. So I forgot about it again.

@stigastondogg730 10 ай бұрын

@@kragiharp ah I see I’m a mechanical engineer, also with a math degree, so haven’t done any circuitry stuff since graduating.

@kevinbush4300 10 ай бұрын

@@stigastondogg730 oh, you'd be amazed at the applications this has, in the real world! (That's what i always say to anyone from the age of seven upwards who asks what's the point in learning all this boring stuff they're never going to use... usually means i haven't a clue)

@beachboysandrew 10 ай бұрын

This video made some linalg stuff clear to me that I'd never really understood so well. Your videos are so good man, please always keep uploading!

@lawrencejelsma8118 10 ай бұрын

It is better to have whole number eigenvectors since they are just scalar multiples. I prefer v1 = (1 + i , 2) and v2 = (i - 1 , 2) eigenvectors vs yours having a 1/2 in them. Neat instruction as always.

@punditgi 10 ай бұрын

Nothing complex about how to learn math. Just watch Prime Newtons! 🎉😊

@ciprianteasca7823 10 ай бұрын

Yes! I wish I was 16, 17 years old again...(well...for other reasons too 🤫)... We stay "tuned"!

@Tenorsax333 10 ай бұрын

The demonstration is very beautiful and completely clear! :) In my opinion, the part from 8:00 to 10:40 shouldn't be done at all. It simply shows (by eliminating the second row) that the first matrix is actually not invertible and therefore its determinant is zero. It would be enough to show this proof once. The calculation could now continue where it was interrupted at 8:00: We can return to the unchanged matrix and choose one of its two rows. If we choose the first one, we get: x1 = 1, x2 = -i+1. These two components look different than the ones the presenter received, but together they represent the first eigenvector v1. (If you don't believe it, multiply this result by (i+1)/2, then you get the two components x1 = (i+1)/2 and x2 = 1, as shown from 12:15.) Likewise, the part from 13:20 to 14:20 could be omitted for the second matrix.

@GautamRishimahadev7 10 ай бұрын

Hy sir I am indian an I studies in class 10th i watch to your videos nice ❤❤

@pietlemao8491 5 ай бұрын

U make maths look easy sir. Please do videos on linear algebra 3 or advanced

@Aryaggg5 10 күн бұрын

Thank you very much!

@zakhelexulu3394 4 ай бұрын

What a nice explaination

@thomasolson7447 2 ай бұрын

Some roots have a rotation in them, others don't. They mix and match. So, in many cases one root contributes to the imaginary value and the doesn't. Or it could go the other way. And I've seen complex roots that only contribute real values. But we're automatically distributing to both parts of the vector x_1 and x_2. Fibonacci numbers is an example. One root is purely real, the other root has a rotation factor in it because logs can't be negative. So, that second root is a complex number when time is a non-integer.

@mil9102 10 ай бұрын

8:51 isn’t the conjugate (-1 - i)? As it’s written as (i - 1) = (-1 + i) hence conjugate is (-1 - i). Guess it’s similar but with minus sign (-1-i) = -(1 + i)

@dukundanejeandedieu7199 5 ай бұрын

good he made mistake kbx

@holyshit922 10 ай бұрын

Yes , but sometimes we dont have full set of eigevectors Matrix is non-diagonalizable in this case

@holyshit922 10 ай бұрын

In Numerical recipes there is code for QR method for eigenvalues but when I rewrite it in C# I get uninitialized variable error Eigenvectors can be found by Inverse power method which uses LU decomposition

@comrade_marshal 10 ай бұрын

What made you choose or rather why have you chosen C#? Just asking

@holyshit922 10 ай бұрын

@@comrade_marshalWindows user simply and C# is built-in up to C# 5

@comrade_marshal 10 ай бұрын

@@holyshit922 i c