Linear preservers of balanced nonsingular inertia classes Original Research Article

Let V be one of the following four real vector spaces: imagen, the n × n real symmetric matrices; imagen, the n × n complex hermitian matrices; image, the n × n real matrices, and image, the n × n complex matrices. Suppose T is an image-linear map on V preserving the invertible matrices in the case image or image or preserving the nonsingular balanced inertia class (n even) in the case V = imagen or imagen. If n> 2 and n ≠ 4 or 8 when image, we show that T must be invertible and specify the exact form of T.