Complex eigenvectors

In this video , I showed how to compute complex eigenvalues and eigenvectors of a matrix with complex entries

[@kragiharp]

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]

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]

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

[@kragiharp]

@@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]

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

[@kevinbush4300]

@@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]

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]

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.

[@GautamRishimahadev7]

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

[@Tenorsax333]

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.

[@pietlemao8491]

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

[@punditgi]

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

[@ciprianteasca7823]

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

[@zakhelexulu3394]

What a nice explaination

[@Aryaggg5]

Thank you very much!

[@thomasolson7447]

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]

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]

good he made mistake kbx

[@holyshit922]

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

[@holyshit922]

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]

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

[@holyshit922]

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

[@comrade_marshal]

@@holyshit922 i c

[@haymanottadele-e7f]

It better video

[@musicphysics-mathematicsfu1840]

You are too much! Which country are you from,if I may ask?

[@PrimeNewtons]

🇳🇬

[@Onlyforfun1992tube]

Guys there is only one god come back to his path Allah loves you now come back to him

[@juv7026]

blasphemy is a sin

[@comrade_marshal]

Come on. This is a math channel. Stop trolling here. Go to some other type of channel