Using power method to calculate dominant eigenvalue and eigenvectors

AI Thread Summary
The discussion focuses on using the power method to calculate the dominant eigenvalue and eigenvectors for given matrices. The user successfully solved the first question but is struggling with the second, particularly after finding an eigenvector that yields the same result repeatedly. There is a suggestion to try a different orthogonal starting vector to potentially uncover a larger eigenvalue. Additionally, there is a question regarding whether to extract the middle or highest value from the matrix during calculations. The conversation emphasizes the importance of exploring multiple starting points in the power method for accurate results.
savva
Messages
39
Reaction score
0

Homework Statement


Use the power method to calculate the dominant eigenvalue and its corresponding eigenvectors for the matrices.
The questions are attached with this thread. I have attempted both and seem to have done the first question correctly. I am attempting the second question and am stuck as after finding one eigenvector I got the same result again. Can anybody help me out with what I have to do here?

Also, when taking out a value from the matrix, should it be the middle value or the highest value in the matrix?

Homework Equations





The Attempt at a Solution

 

Attachments

Physics news on Phys.org
Sounds like you found an eigenvector with eigenvalue 1, congratulations :-)

But you should probably try another, orthogonal, start vector too to see if there's another larger eigenvalue.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

How Do Eigenvalues and Eigenvectors Change for Matrix B = exp(3A) + 5I?
Replies
14
Views
2K
Find an appropriate matrix according to specific conditions
Replies
8
Views
2K
I Can one find a matrix that's 'unique' to a collection of eigenvectors?
Replies
33
Views
726
I Unravelling Structure of a Symmetric Matrix
Replies
5
Views
2K
I Getting eigenvalues of an arbitrary matrix with programming
Replies
1
Views
2K
A The eigenvalue power method for quantum problems
Replies
2
Views
2K
I The Orthogonality of the Eigenvectors of a 2x2 Hermitian Matrix
Replies
13
Views
3K
Linear Algebra: 2x2 matrix raised to the power of n
Replies
9
Views
7K
Engineering How do I find the transition matrix of this dynamic system?
Replies
18
Views
3K
Find eigenvalues & eigenvectors
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top