I have a question regarding the eigenvalues of a block Hermitian matrix as a function of the eigenvalues of the diagonal block matrices and the off-diagonal matrices. In particular, I am interested in the 2x2 block case.
I have checked some previous posts [1]: Eigenvalues of certain block hermitian matrix and in Wikipedia, and it is clear to me that the solution for the case M1=(ABBA), where M1, A and B are Hermitian, can be derived.
Nevertheless, I would like to know if it is possible, in the following case: M2=(ABBHC) where M2, A and C are Hermitian and B corresponds to the off-diagonal block, to say something about the eigenvalues of M2 as a function of the eigenvalues of A and C and the matrix B.
Best regards.
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