Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (23 of 35) The Power Method with Scaling

In this video I will find the dominant eigenvector and the corresponding eigenvalue using the power method with scaling (2x2 matrix).

Next video in this series can be seen at:

[xavianmarotta]

This was exactly what I needed, someone who actually does a problem instead of explaining confusing concepts. This helped me extremely, thank you very much.

[ZaChousenWan]

What is the purpose/uses of finding the dominant eigenvector of a matrix?

[mrarcticaaa]

Now this was cristal clear. Thank you so much.

[mdraza]

Thank you so much sir....This lecture clearly resolves all my doubt....for eigenvalues and eigenvectors

[malintha]

This is brilliant! Thank you for the nice tutorial!

[Nissearne]

Thanks. Great tutorial.
I wounder how is it possible to find the eigenvectors with lower eigenvalues in a order. Say I have a 10x10 Transformation how will I find the top 5 eigenvectors in order of that 10x10 matrix ?
Is there a similar "Power Method" to solve that kind of problem ?

[alyahayani]

does this method same with shifted power method?

[Nissearne]

Thanks again.
Regarding my last question (how to get out several other eigenvectors how are smaller then the strongest eigenvector?)
Could it possible be a way to use this eigenvector to some sort of dimension reduction (rotation and subtraction or something ?) of the matrix to a lower order of dimension then continue to do the same method again ? Or am I total wrong?
Best Regards
Olle Welin