Point product

The point-by-point product in mathematics is an inner two-digit link which, in addition to the convolution , is understood as the product of two functions . The point-by-point product is only defined if the image quantities are chosen so that all elements can be multiplied with one another. ${\displaystyle \operatorname {Bild} (f),\;\operatorname {Bild} (g)}$

definition

Let and function with the map If a multiplication is well defined , then the pointwise product is fixed as ${\displaystyle f}$ ${\displaystyle g}$ ${\displaystyle X\to Y.}$ ${\displaystyle \cdot \colon Y\times Y\to Y,\;y_{1}\cdot y_{2}\mapsto \mathrm {z} }$

${\displaystyle (f\cdot g)(x)=f(x)\cdot g(x)}$.

application

Pointwise products can be used to define vector spaces with functions. Other algebraic structures can also be defined that contain, for example, rings or solids on which a multiplication is defined.