diagonalization using unitary matrices

Dear All

I have got a self adjoint square matrix with real coefficients and I
need to find the unitary matrix which diagonalizes the first.
According to the spectral theorem such unitary matrix exists but the
traditional method of diagonalization, which consists in finding the
eigenvectors and putting them as the columns of a diagonalization
matrix does not generate necessarily an unitary matrix.

Anyone knows how to solve this?

Thanks

math_think
.

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