I need some help with the following:
Consider the sequence
1) Write an expression for the eigenvectors of using the eigenvectors of . Then use this to write an expression for the eigenvectors of using the matrices , and the eigenvectors of .
I am completely lost and have no idea where to start. Any pointing me in the right direction would be greatly appreciated!
edit: I can't get line breaks to work in the above code...(?)
Tonio, thank you! You saved my day!
Here's my take on the second part ("Write an expression for the eigenvectors of using the matrices , and the eigenvectors of ).
(I'm using and instead of and , respectively.)
From the first part we now have: . Obviously would be (1) ,
... and so on...
Inserted into (1), we get:
Thus a pattern evolves:
where is the eigenvector of , i.e.
Does that look somewhat alright? Something I've missed? Or better ways to write it? (especially (2))...