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I need a Real an Imaginary part as real numbers, to find eigenvalues and eigenvectors with my solver, which works only with Real matrices.

My matrix element is:

[tex]M_{mn}=\int^{tk}_{0} -i Exp[i E_{mn} t] V_{mn}(t) dt[/tex]

The integrals are easy to write, but are complex.

I want to write matrix M as new matrix of dimension 2N to find eigenvectors and eigenvalues of that matrix, which are also complex.