On Some Applications of Lidskii's Theorem

Lidskii's theory is considered one of the most important and recent theories for calculating the following categories and the relationship between them and the eigenvalues. This theory provides an easier way to prove the existence of the eigenvalues, and hence to prove the existence of solutions for some kind of problems. This thesis article to prove that there are solutions to some problems for which the computation of eigenvalues is very complex and to prove that the existence of eigenvalues is also complex, in our work we try to take advantage of the fact that calculating the trace is much easier than calculating eigenvalues. Lidskii's theorem gives the relationship between Trace and eigenvalues and gives us a way to prove the existence of eigenvalues.