1 Eigenvalues of the sum of matrices from unitary similarity orbits

By Chi-Kwong Li, Yiu-Tung poon and Nung-Sing Sze.

Let A and B be n × n complex matrices. Characterization is given for the set E(A, B) of eigenvalues of matrices of the form U^{∗}AU + V^{∗}BV for some unitary matrices U and V. Consequences of the results are discussed and computer algorithms and programs are designed to generate the set E(A, B). The results refine those of Wielandt on normal matrices. Extensions of the results to the sum of matrices from three or more unitary similarity orbits are also considered.