Linear polynomial in the context of Nonnegative integer

In mathematics, a linear equation is an equation that may be put in the form${\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0,}$ where ${\displaystyle x_{1},\ldots ,x_{n}}$ are the variables (or unknowns), and ${\displaystyle b,a_{1},\ldots ,a_{n}}$ are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients ${\displaystyle a_{1},\ldots ,a_{n}}$ are required to not all be zero.

Alternatively, a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken.

In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper.

The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. In category theory, a map may refer to a morphism. The term transformation can be used interchangeably, but transformation often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory.