# B What does this set notation mean?

1. Mar 12, 2016

### pellman

$$A \oplus B$$

where A and B are sets

2. Mar 12, 2016

### HallsofIvy

That is not a standard notation for sets. It can mean a direct sum for sets with sum kind of "sum" defined, such as vector spaces. Is that what you mean?

3. Mar 12, 2016

### pellman

Actually, yes, in the context it was used the sets in question are subspaces of a vector space.

The context is page 137 here http://perso.crans.org/lecomtev/articles/Brian_Hall_Quantum_Theory_for_Mathematicians_2013.pdf [Broken]

Last edited by a moderator: May 7, 2017
4. Mar 12, 2016

### PeroK

https://en.wikipedia.org/wiki/Hilbert_space#Direct_sums

Last edited by a moderator: May 7, 2017
5. Mar 12, 2016

### pellman

6. Mar 12, 2016

### HallsofIvy

The "direct sum" of two vector spaces, A and B, (both subspaces of some vector space, V) is the smallest subspace that contains all the vectors in both A and B. Another way of doing that is to construct bases for both A and B, combining them and then reducing to a set of independent vectors to get a basis for $A\oplus B$.