Designating matrices by (system2 operator system1)

[Lojzek]

Hi,

I already posted this in solid state physics forum, but no one answered, so I guess this topic might belong to Mathematics.

I read a text about crystallography where matrices were designated in the form:

(S2 O S1)

where S1 is input coordinate system, S2 is output coordinate system and O is the linear operator corresponding to the matrix. I found this designation is often more useful than the usual matrix designation by a capital letter (which omits information about coordinate systems): in particular, matrix transformations between different coordinate systems are made particulary transparent.

Does anyone know whether this designation is common in mathematics?
If so, in what area of mathematics is it used? Please provide links if possible.
(I would like to know this because I am using this designation in my graduation work)

 

[fresh_42]

Does anyone know whether this designation is common in mathematics?

It is not.

If so, in what area of mathematics is it used?

It would be in Linear algebra, but it isn't used. At least what I can deduce from your sparse description of the $S_i$. It looks like a linear transformation of a vector space of tensors.