A puzzle

We have learned that if a matrix A has an eigenvector v to an eigenvalue L, then B=A¹⁰ has an eigenvalue L¹⁰ to the same eigenvector. A student checked this with the computer and sent in the following screen shot. Obviously the eigenvectors of B are not the same then the eigenvectors of A. It is your task to solve the puzzle!

Please send questions and comments to knill@math.harvard.edu

Math21b Harvard College Class Number:16325 Course ID:110989| Oliver Knill | Spring 2016 | Department of Mathematics | Faculty of Art and Sciences | Harvard University, [Canvas, for admin], Twitter