Circled minus sign

  • #1
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16

Main Question or Discussion Point

This should be really easy, but I can't seem to find the answer. What does the symbol ##\ominus## mean in the context of Hilbert spaces? As in "##H \ominus A##" where H is a Hilbert space and A is presumably a subspace or subset of H. I'm guessing it's like the inverse of a direct sum, ##\oplus##? As in, if ##H = A \oplus B##, then ##H \ominus A = B##. Is that correct?
 

Answers and Replies

  • #2
525
16
Did some more searching and found the answer here. One of the answers there says:

If ##A \subset B## are linear subspaces of a Hilbert space, ##B \ominus A = \{x \in B: (x,y) = 0 \text{ for all }y \in A\}##. ##\ominus## is also used for the symmetric difference of sets.
 
  • #3
HallsofIvy
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Thanks for posting that. So "[itex]A\oplus B[/itex]" is the "orthogonal complement" of B in A.
 

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