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.
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 :
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.