# What do these two symbols mean?

I was looking into a set of equations, and came across two different symbols that I'm not familiar with what do they mean? One looks like an "X" inscribed in a circle and the other was an addition sign in scribed in a circle. Again, what do they mean?

Where did you come across these symbols? Although the meaning of many symbols are universal, some may depend on the context.

What you're referring to seems like the operations of a field, for example - http://mathworld.wolfram.com/Field.html. If it is so, the 'x in a circle' is called multiplication and the + is known as addition, although these need not always represent the multiplication and addition that we use in our daily lives.

I don't remmber the exact site, but it seems like it was talking about tensors.

It could be tensor products. But I'm not well-versed in tensors, so I'll leave this up to someone who know tensors well.

Tom Mattson
Staff Emeritus
Gold Member
I was looking into a set of equations, and came across two different symbols that I'm not familiar with what do they mean? One looks like an "X" inscribed in a circle
As neutrino has suggested, this is indeed the tensor product. It's fairly simple to write down for matrices, and they do so here:

http://en.wikipedia.org/wiki/Tensor_product

and the other was an addition sign in scribed in a circle. Again, what do they mean?
This is the direct sum of two modules. This may be in your linear algebra book, but it would be known as the direct sum of two vector spaces. This is just a special case of the direct sum of modules, as a vector space over a field F is just an F-module.

http://en.wikipedia.org/wiki/Direct_sum