Cubic Idempotence Preserver Problem in Hermitian Matrix Space

Preserver problems are the study of preserving maps of certain invariants on a given mathematical structure. In order to preserve the cubic idempotent of Hermitian matrix space, we study the image from the basis of 2 × 2-dimensional Hermitian matrix space to m × m-dimensional Hermitian matrix space, and give the representation of the real linear mapping from low-dimensional to high-dimensional Hermitian matrix space.