Designating matrices by (system2 operator system1)

[Lojzek]

Hi,

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 operator
corresponding to the matrix. I found this designation is often more useful than the
usual designation by capital letter (which omits information about coordinate systems).

Does anyone know whether this designation is used only in crystallography or is it common in mathematics? Does it have a name? Please provide links if possible.

 

[eljose79]

Hello,

Thank you for your interest in crystallography and the use of matrices in this field. The designation you mentioned, (S2 O S1), is commonly used in crystallography to represent matrices. This notation is also used in mathematics and is known as the "coordinate-free" notation or "Einstein notation". It is a more comprehensive and informative way of representing matrices, as it includes the coordinate systems involved in the transformation.

This notation is not limited to crystallography and is also used in other fields such as physics and engineering. It is especially useful in fields where multiple coordinate systems are involved, as it helps to keep track of the transformations between them.

Here are some links that further explain this notation and its usage:

1. https://en.wikipedia.org/wiki/Einstein_notation
2. https://www.mathworks.com/help/symbolic/einstein-summation.html
3. https://www.sciencedirect.com/topics/chemistry/crystallography

I hope this helps clarify your doubts. Let me know if you have any further questions.