Need to solve in mat lab please help For the matrixes A below, find a factorizat

Question

Need to solve in mat lab please help

For the matrixes A below, find a factorization of A in the form A=PCP-1 or A=PDP-1 where C is a block-diagonal matrix with 2 Times 2 blocks of the form and D is a diagonal matrix D. Consider that the matrices P, C, D have real entries. Discuss your results (why did you obtain one type of factorization or the other; can you obtain both types of factorization for the same matrix). Hint: For each conjugate pair of eigenvalues, use the real and imaginary parts of one eigenvector in C4 to create two columns of P. Hint: Use the eig command to create the diagonal matrix D and find eigenvectors to create an invertible matrix P.

Explanation / Answer

A=[1 5;-2 3];
[V,D]=eig(A)
P=[real(V(:,1)) imag(V(:,1))];
C=[real(D(1,1)) imag(D(1,1)); -imag(D(1,1)) real(D(1,1))];
P*C*inv(P) %We can check our work- We should get A back

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