Linear

Biography & Overview

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 . {displaystyle aX+bY+cZ+d.} Linearity of a mapping is closely related to proportionality. Examples in physics include the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight.