Hi everybody,

I don't know how to solve the following problem. I have rewritten the things according to the hint, but couldn't make much use of it.

Lemma:

Let and and denote by the rows of . Then

(Tr is the trace of a matrix)Thank you very much!Now prove that the solution of

are the first eigenvectors of a symmetric matrix :

Hint:

Use the fact that is a symmetric matrix and therefore has the representation , where is an orthogonal matrix where the columns of contain the eigenvectors of and is a diaogonal matrix that contains the eigenvalues on the diagonal. Then use the lemma.