I am going through a course in linear algebra. Most of the time I learn that "this concept can be generalized to complex matrices without loss of generality" or "since it holds for complex matrices, it holds for real matrices also". I was curious if there are any concepts that holds for real matrices and doesn't hold for complex matrices and vice-versa.
Some trivial ones are
- Determinant and trace of a real matrix is real
- Eigen values occurs in complex conjugate pairs.
- Fundamental spaces associated with a real matrix are all real.
thats it!!, that's all I could remember now. Any help would be appreciated.