Matrices - Eigenvalues/vectors/diagonalisation

[Ashbearify]

Can you tell me... What are the strengths and limitations of using diagonalisation of matrices.

[burny1]

@Ashbearify They are good at solving functions as in this video /watch?v=JC3KmZGkc9w . However if there are a large number of variables and/or a large matrix it is very difficult without the use of a computer to solve the simultaneous equations. Not to mention finding the determinant becomes time consuming also. But for smaller matrices it can be quite simple.

[Ninjarni]

what just happened...? fairly unclear explanation

[orpawil]

from where did u get x1 times the metrix (1,1) at 4:56 minutes ??

[burny1]

@orpawil i'm just taking the x1 out of the eigenvector (x1,x1) we have found so x1 can just multiply to be anything. eg we could say it is 2 and use (2,2). because we decided that inorder for (A-I)x=0 x needs to have both x1 and x2 same

[FistsofVengeance]

thanks for sharing mate

[VanillaShoelace]

wats a vekter

[hitman122967]

OMG....THANK YOUUUUU SOOO MUCH.... u just save my ass before my midterm exam ^_^

[cmmadnat]

Thank you very much. i'll have an exam about this tomorrow, on my Information Retrieval Course, this eigenvalues and eigenvectors cause me a very hard time!

[mcgooo1]

thanks a lot man you helped me a lot!!

[curioustoknow123]

@Teoteomusik ,

what part didnt you get?

[Teoteomusik]

i didnt get eigen vector,... :(

[gladstonereal]

oops sorry due to the 0 i understand now it will amount to zero.....great job!

[gladstonereal]

i think u should have had λ^2 - 3λ + 3 due to the subtraction of the -1

[daverandomster]

it becomes zero (-1*0=0)

[Brianaust138]

Thanks, that's great video.

But,

I didn't understand how did you find " λ^2 - 3λ + 2 "??

[69erthx1138]

He multiplied (1-λ) and (2-λ) together. That quadratic equation is called the characteristic equation. Actually all you have to do is look at what is added or subtracted from in the primary matrix elements to determine the eigenvalues.

[kenrubes]

nice, but it might be cool to really stress that the singular matrix ==> nontrivial eigenvectors. Most students generally have no idea why they're doing what they're doing.

[sting695]

his explanation for eigenvectors was poor! everything else was great...

[Cyzos1]

Thanks a lot, man... I would've been boned without this

[magiccomputer]

i have a question  only eigen values and eigen vector not diagonalisation.

[burny1]

i dont understand your question sorry. diagonaliseation is at the end of the video

[surflife91]

hey thanks for the video, really helpful with the exams cumin up n all!

[dacoolest123123]

hey lets say you have a 3 by 3 matrix you get the characteristic polynomial can you then row reduce to make the determinent easier?

[burny1]

Yes. Lecture 14 on the website

[benparker23]

Great Video. Thank you.

[MathHelpNeeded]

since x=z the last example given at 9:05 minutes shows the different values for P, but x=2 and z=4 so how does that work?

[burny1]

thanks for that. was a case of me copying the matrix and forgetting to change that 4. thanks

[Navigator20081]

thanks alote