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Tuesday, February 2, 2010

Matrix of Mappings

I recently published new paper
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 = x2 then
f(x)dx=(x1+1x)dx=x dx+dx x

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