09-20-2021-0914 - Antilinear Map conjugate-linear conjugate linear

In mathematics, a function  between two real or complex vector spaces is said to be antilinear or conjugate-linear if

where  and  are the complex conjugates of  and  respectively. 

Antilinear maps occur in quantum mechanics in the study of time reversal and in spinor calculus, where it is customary to replace the bars over the basis vectors and the components of geometric objects by dots put above the indices.

https://en.wikipedia.org/wiki/Antilinear_map

In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An equivalent statement that implies incompressibility is that the divergence of the flow velocity is zero (see the derivation below, which illustrates why these conditions are equivalent).

Incompressible flow does not imply that the fluid itself is incompressible. It is shown in the derivation below that (under the right conditions) even compressible fluidscan – to a good approximation – be modelled as an incompressible flow. Incompressible flow implies that the density remains constant within a parcel of fluid that moves with the flow velocity.

https://en.wikipedia.org/wiki/Incompressible_flow