Generalization to complex E-eigenpairs

Determine whether the proof strategy developed for real Z-eigenpairs of regular simplex tensors can be generalized to E-eigenpairs over the complex field.

Background

The paper establishes the existence and uniqueness characterization of robust Z-eigenpairs for regular simplex tensors over the real field, using a connection between tensor-power-method robustness and local optimality. Its analysis relies on real constrained optimization and the structure of real eigenpairs.

The authors explicitly identify the extension from real Z-eigenpairs to complex E-eigenpairs as unresolved. Such a generalization would require determining whether the proof strategy, including the local-optimality reduction and optimization-landscape analysis, remains valid in the complex setting.