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

Staff Emeritus
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

Staff Emeritus
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 $A\oplus B$.

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