Linear - Maple Help

define/linear

define characteristics of a Linear operator

 Calling Sequence define(L, linear)

Parameters

 L - name of the linear operator being defined

Description

 • define/linear sets up a definition of L which allows simplification and evaluation.
 • The properties of a linear operator are:

$L\left(\mathrm{K1}a+\mathrm{K2}b\right)=\mathrm{K1}L\left(a\right)+\mathrm{K2}L\left(b\right)$

$L\left(\mathrm{K3}\right)=\mathrm{K3}L\left(1\right)$

$\mathrm{for any}\mathrm{constants}\mathrm{K1},\mathrm{K2}\mathrm{and}\mathrm{K3}$

Examples

 > $\mathrm{define}\left(L,'\mathrm{linear}'\right)$
 > $L\left(5\right)$
 ${5}{}{L}{}\left({1}\right)$ (1)
 > $L\left(3x+z\right)$
 ${3}{}{L}{}\left({x}\right){+}{L}{}\left({z}\right)$ (2)
 > $L\left(\mathrm{\pi }\right)$
 ${L}{}\left({\mathrm{\pi }}\right)$ (3)