eprint arXiv:1001.4852 The Matrix of Linear Mappings, 2010

In this paper, I consider change in notation of mapping. Instead of notation

y=f(x)

I use notation

y = f ° x

Let us consider ring of mappings of R-algebra A with product f ° g

This point of view allows me to consider ring R as representation in algebra A. If f is additive mapping of algebra A then I can write value of map in form f ° h. In particular I can write derivative of mapping of algebra in form

∂f(x)(h)=∂f(x) ° h

This allow me to separate derivative and increment of argument. In this case I need to use tensor notation for derivative. For instance, if f ° x = x

^{2}then

$$\partial f(x)\circ dx=(x\otimes 1+1\otimes x)\circ dx=x\ dx+dx\ x$$