the task is following:
Let's assume that vector is eigenvector corresponding to eigenvalue of matrix . Also corresponds to eigenvalue of matrix . Now the questions:
I Is the eigenvector of matrix ?
II Is the eigenvector of matrix ?
If answer is yes to atleast one question, it must be shown, to which eigenvalue vector corresponds.
I think I should use following theorem:
"If is eigenvector corresponding to eigenvalue of matrix , then is is eigenvector corresponding to 's ".
But somehow, I can't get anywhere, though I inspected eigenvalues and -vectors definitions closely. Also it's no problem to me calculate those vectors and values in normal cases. So, any help is appreciated. Thank you!