An example of what I am talking about is indicating multiplication by writing
$$ab\equiv{a}\times{b},$$
in traditional real number algebra.
I was writing some notes involving matrix multiplication. Previously in these notes I had specified that placing two tensor symbols next to each other indicates a direct product. For example:
Let $\mathfrak{A}=\left\{A_{ij}\right\}_{n\times{n}}$ and $\mathfrak{v}=\left\{v_{k}\right\}_{n\times{1}}.$ So in the context of my definition:
$$\mathfrak{A}\mathfrak{v}\equiv{\mathfrak{A}\otimes\mathfrak{v}}\equiv{\left\{A_{ij}v_{k}\right\}_{n\times{n}\times{n}}}.$$
But when working with matrices in linear algebra it is common practice to use
$$\mathfrak{A}\mathfrak{v}\equiv{\left\{\sum_k A_{ik}v_{k}\right\}_{n\times{1}}}.$$
Well, I want to use the latter definition in one example. When I tried to state that placing the symbols next to each other without any operator symbol between them means matrix multiplication in this example, I found that I have no formal terminology for doing that. I started to say "the juxtaposition of symbols…", but when I looked up the work juxtapose, I realized it's not what I mean. It connotes an intent to compare and contrast.
Is there a formal term for implying an operation by placing two symbols next to each other?
Best Answer
In abstract algebra, when words are formed using letters from an alphabet, the operation of joining two words together with no symbol in-between is called concatenation.
Now I wouldn't recommend that in a case where the left and right sides are mathematical objects of a different nature. In that case, it seems that juxtaposition is fine - I have seen it used at least a couple of times, and I don't feel that it carries a connotation in a mathematical context. And if you want to be extra clear, you can add some words the first time you use it, in a footnote for instance.