Linear function

In mathematics, the term linear function refers to two distinct but related notions:[1] In calculus, analytic geometry and related areas, a linear function is a polynomial of degree one or less, including the zero polynomial (the latter not being considered to have degree zero).

of any finite number of variables, the general formula is and the graph is a hyperplane of dimension k. A constant function is also considered linear in this context, as it is a polynomial of degree zero or is the zero polynomial.

In the context of linear algebra, the polynomial functions of degree 0 or 1 are the scalar-valued affine maps.

In linear algebra, a linear function is a map f between two vector spaces such that Here a denotes a constant belonging to some field K of scalars (for example, the real numbers) and x and y are elements of a vector space, which might be K itself.

In other terms the linear function preserves vector addition and scalar multiplication.