I'm building a library in C for embedded systems that can compute linear algebra. Available on my GitHub.
I'll write code for the library to use eigenvalues and eigenvectors, including Schur decomposition. However, I do not know if I should write code so that the algorithm can compute the complex eigenvalues, or should I focus only on the real part of the eigenvalues.
I remember my engineering and control theory class, where we compute the complex eigenvalues, but we only have the real part of those values.
Code in algorithms that can calculate complex eigenvalues and eigenvectors requires a lot of time for the microcontroller. So my question to you is how important complex eigenvalues are in real problems. Or are we just looking after the real part?