feat(data/complex/module): define `real_part` and `imaginary_part` (#16438)
feat(data/complex/module): define `real_part` and `imaginary_part` (#16438)

In a generic `star_module` one always has a decomposition of any element into a `self_adjoint_part` and a `skew_self_adjoint` part, but in a star module over `ℂ` we can instead decompose any element into a `real_part` and an `imaginary_part`, both of which are self-adjoint. Here we define these as `ℝ`-linear maps from the star module into the type of its self-adjoint elements and describe the basic relationships between these maps. The decomposition into real and imaginary parts is often useful for reducing arguments about elements of a star module over `ℂ` to the case when the element is self-adjoint.





leanprover-community/mathlib,leanprover-community/mathlib