Exercises section 10.3

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(1)  For the matrix A, the eigenvalues are given. Find an orthogonal matrix P such that
       is a diagonal matrix :
            
    
    
      

                                                                                                                                                    

(2)  Find the spectral decomposition of the following:
   
             

                                                                                                                                                   

(3)  Let A be a real symmetric matrix with P such that P is orthogonal and  ,
       diagonal. Show that is also diagonalizable by an orthogonal matrix, there exists
       orthogonal matrix such that Find the relations between and P,
       and .

                                                                                                                                                   

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