10.3.2 Corollary:
Let A be n n real symmetric matrix such that all its eigenvales are distinct. Then, there
exists an orthogonal matrix P such that
                                  
,
where D is a diagonal matrix with diagonal entries being the eigenvalues of A.

                                                                                                                                               

Proof of Corollary 10.3.2

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Let  A has eigenvalues
By  corollary , the matrix
                               
is invertible and , is diagonal with diagonal entries ..........
Further, by theorem 10.3.1, is an orthogonal set. Hence P is in fact an orthogonal
matrix.