dFij
dFij is a notation used in differential calculus to denote the differential of the ij-th component of a matrix-valued function F. It is not a single universally standardized symbol, but a convenient shorthand that appears in contexts where F takes values in a matrix space and its individual components are studied separately.
Definition and usage. If F maps a domain X into matrices of size n by m, with
Example. Let F(x, y) = [[f11(x, y), f12(x, y)], [f21(x, y), f22(x, y)]]. Then dF = [[df11, df12], [df21,
Relation to other concepts. dFij is related to the broader idea of matrix-valued differential forms and to
See also. differential, differential form, matrix-valued function, deformation gradient, tensor calculus.