We discuss a method for solving complex symmetric (nonHermitian) eigenproblems Ax = λBx arising in an application from optoelectronics, where reduced accuracy requirements provide an opportunity for trading accuracy for performance. In this case, the objective is to exploit the structural symmetry. Consequently, our focus is on a nonHermitian tridiagonalization process. For solving the resultin...

We discuss an extension of the almost Hadamard matrix formalism, to the case of complex matrices. Quite surprisingly, the situation here is very different from the one in the real case, and our conjectural conclusion is that there should be no such matrices, besides the usual Hadamard ones. We verify this conjecture in a number of situations, and notably for most of the known examples of real a...

We consider an ensemble of large non-Hermitian random matrices of the form Ĥ + iÂs, where Ĥ and Âs are Hermitian statistically independent random N × N matrices. We demonstrate the existence of a new nontrivial regime of weak non-Hermiticity characterized by the condition that the average of NTrÂs is of the same order as that of TrĤ 2 when N → ∞. We find explicitly the density of complex eigenv...