I have 3 eigenvectors for a matrix M, I have normalised them so that U^t*M*U is a diagonal matrix (U^t is the transpose of U).

How do i know which eigenvector goes in which column of U.

Also I have been asked to find the diagonal matrix formed by U^t*M*U.

Is there any way to make this easier to find, as this will require multiplying a lot of fractions with surds everywhere...