We are developing some computer program which at some point uses a library (for which we do not have access to its source code) to solve the general eigenvalue problem; given two input real symmetric matrices $A$ and $B$, calculate eigenvalues $\lambda$ and eigenvectors $v$.
Then we need to test another library which performs the same calculation. The initial problem is that it only accepts as input hermitian matrices.
Therefore we wonder if we could somehow convert our real matrices $A$ and $B$ to hermitian. I guess we would need to specify zero for the imaginary part of the complex number.