Designating matrices by (system2 operator system1)

In summary, the conversation is asking about the common use of a particular designation for matrices in mathematics, specifically in the area of crystallography. The designation involves input and output coordinate systems and a linear operator. The person asking is using this designation in their graduation work and is looking for more information and possible links. The response is that this designation is not common in mathematics, but it would potentially be used in linear algebra for linear transformations of vector spaces of tensors.
  • #1
Lojzek
249
1
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)
 
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  • #2
Lojzek said:
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.
 

1. What is the significance of designating matrices by (system2 operator system1)?

Designating matrices by (system2 operator system1) is a way to represent mathematical operations on a matrix using two different systems. This allows for a more efficient and organized way of performing calculations and analyzing data.

2. How does designating matrices by (system2 operator system1) differ from traditional matrix notation?

Unlike traditional matrix notation, where operations are performed using only one system, designating matrices by (system2 operator system1) allows for the use of two systems simultaneously. This can provide more flexibility and accuracy in calculations.

3. Can any type of matrix be designated by (system2 operator system1)?

Yes, designating matrices by (system2 operator system1) can be applied to any type of matrix, including square matrices, rectangular matrices, and even complex matrices.

4. How does this method impact matrix operations?

Designating matrices by (system2 operator system1) can simplify and streamline matrix operations. By using two systems, it allows for a more organized approach to calculations and can help identify patterns and relationships within the data.

5. Are there any limitations to designating matrices by (system2 operator system1)?

While this method can be very useful, it may not be suitable for all situations. It may not be necessary or practical to use two systems for simple matrix operations, and it may also require a deeper understanding of both systems in order to accurately apply them to the matrix.

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