1.Previous
3.Next

is additive but not homogeneous. The conditions of additivity and homogeneity are often combined in the superposition principle

An equation written as

is called linear if is a linear map (as defined above) and nonlinear otherwise. The equation is called homogeneous if and is a homogeneous function.

The definition is very general in that can be any sensible mathematical object (number, vector, function, etc.), and the function can literally be any mapping,

1.Previous
3.Next