Using power method to calculate dominant eigenvalue and eigenvectors

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SUMMARY

The discussion focuses on using the power method to calculate the dominant eigenvalue and its corresponding eigenvectors for given matrices. The participant successfully identified an eigenvector with an eigenvalue of 1 but encountered difficulties in finding additional eigenvectors. It is recommended to utilize an orthogonal starting vector to explore the possibility of discovering a larger eigenvalue. The participant also inquired about the appropriate value to extract from the matrix, questioning whether it should be the middle or highest value.

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  • Understanding of eigenvalues and eigenvectors
  • Familiarity with the power method algorithm
  • Basic knowledge of matrix operations
  • Concept of orthogonal vectors
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  • Research the power method for eigenvalue computation
  • Learn about orthogonal starting vectors in the context of eigenvalue problems
  • Explore the implications of matrix value selection on eigenvalue calculations
  • Study convergence criteria for the power method
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Students studying linear algebra, mathematicians, and data scientists involved in eigenvalue problems and matrix computations.

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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

 

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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.
 

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