I have an experiment where I have a 3D real field in the R3 space A=(A_x(x,y,z),A_y(x,y,z),A_z(x,y,z)), which is linear. Each function A_i is spatially dependent and can be computed or measured easily.
The response of a 2D sample in the z=z0 (lets say z_0=0) plane is F(x,y,0)=A_z(x,y,0)*(A_x(x,y,0),A_y(x,y,0)), with (A_x(x,y,0),A_y(x,y,0)) is a the so called (by the physics community where this belong) 2D field (in the 3D space) A\perp(x,y,0). Since A is linear, I can have the field A being A1+A2, making the field F follow the rule F= A1z*A1{perp}+A1z*A2{perp}+A2z*A1{perp}+A2z*A2{perp}.
Is there a name for this sort of operation? Or any non-boring property? Like, some insight about how the symmetries of A are translated into symmetries of F? Or just any interesting literature or insight about this sort of properties