Have you realized the form of linear function? It is written in f(x) = a bx. It has a straight line on the graph. Moreover, it owns a dependent variable and one independent variable. The y refers to the dependent variable, while x is the independent one.
The linear maps should be the values of scalar field if it earns the term linear function according to several writers. people also name this situation as a linear functional.
A linear map is associated with functional analysis and algebra. it is often defined in distinct meaning. people often call it as a linear form or homogenous linear function.