Construct a complex Hermitian matrix by setting j = sqrt(1); A = rand(5) + j rand(5); A
Chapter 6, Problem 19(choose chapter or problem)
Construct a complex Hermitian matrix by setting j = sqrt(1); A = rand(5) + j rand(5); A = (A + A_ )/2 (a) The eigenvalues of A should be real. Why? Compute the eigenvalues and examine your results, using format long. Are the computed eigenvalues real? Compute also the eigenvectors by setting [X, D] = eig(A) What type of matrix would you expect X to be? Use the MATLAB command X_ X to compute XHX. Do the results agree with your expectations? (b) Set E = D + j eye(5) and B = X E/X What type of matrix would you expect B to be? Use MATLAB to compute BHB and BBH . How do these two matrices compare? 2
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