Abstract:
The research deals with a systematic provision of mathematical algorithms to
solve eigenvalue inequalities bounding the sum of eigenvalues of Hermitian
matrices. We study the problem of defining the set of eigenvalues of sum of
Hermitian matrices and then investigate the relationship existing between the
eigenvalues of ni × nj Hermitian matrices A and B to the eigenvalues of their
summand H = A + B. The recent solution appears to deal with the situation
of eigenvalue inequalities where r = n − 2. We modified a number of numerical
methods to formulate inequalities connecting sum of r eigenvalues for H in
relation to sum of r eigenvalues for both A and B depending on the parameters
for r < n where r = n − 1, n − 3. Lastly, the research showed the solution of
possible eigenvalues of sum of Hermitian matrices of size Hn
r for n ≤ 12. Other
gaping issues were also specified
