What does this set notation mean?

[pellman]

$$
A \oplus B
$$

where A and B are sets

 

[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?

 

[pellman]

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?

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

 

[PeroK]

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

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

 

[pellman]

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

Thank you. This is likely what was meant

 

[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 $A\oplus B$.