Linear Function

In calculus, geometry, and plotting contexts, the term "linear function" means a function whose graph is a straight line, i.e., a polynomial function of degree 0 or 1. A linear function in one variable therefore has the form

(1)

while a linear function in variables has the form

(2)

In linear algebra and functional analysis, a linear function is a function which satisfies the linearity conditions

(3)

and

(4)

for all and in the domain and all scalars .