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


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