Linearity

In mathematics, the term linear is used in two distinct senses for two different properties:

linearity of a function (or mapping); linearity of a polynomial. An example of a linear function is the function defined by

    f
    (
    x
    )
    =
    (
    a
    x
    ,
    b
    x
    )
  

{\displaystyle f(x)=(ax,bx)}

that maps the real line to a line in the Euclidean plane R2 that passes through the origin. An example of a linear polynomial in the variables

    X
    ,
  

{\displaystyle X,}




  
    Y
  

{\displaystyle Y}

and

    Z
  

{\displaystyle Z}

is

    a
    X
    +
    b
    Y
    +
    c
    Z
    +
    d
    .

Extends: [Physical phenomena](https://wikipedia.org.ai/Physical phenomena), [Broad-concept articles](https://wikipedia.org.ai/Broad-concept articles)