# Complex matrix to Block Matrix

#### Gaso

How can I redefine my Complex matrix to a Block matrix, similar as matrix representation of complex number.
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:
$$M_{mn}=\int^{tk}_{0} -i Exp[i E_{mn} t] V_{mn}(t) dt$$
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.

#### fresh_42

Mentor
2018 Award
We basically have the situation $M=A+iB$. In order to diagonalize $M$ or to use some normal form, we need to know something about the components $A$ and $B$. If we find a normalization for $A$, it could well ruin the structure of $B$ and vice versa. So in any case, the question isn't answerable in this generality. Moreover, complex calculations are usually better than real ones, since we have more eigenvalues available.

"Complex matrix to Block Matrix"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving