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What does A^(⊥) mean?

  1. Nov 29, 2012 #1
    I'm looking at a condition in a maths paper that I don't understand, essentially it is:

    x ∈ R ⊕ R

    R is a set I think, but I'm not sure what the perpendicular symbol means.

    Also am I correct in thinking the circled plus means that x must be in either R or R (but not both)?

  2. jcsd
  3. Nov 29, 2012 #2


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    Homework Helper

    The upside down capital T means <perpendicular>, both in elementary geometry and in linear algebra (or functional analysis). A to the power T upside dowm is the subset B of M made up of all y in M, such that whatever x from the subset A of M, <x,y> = 0, where (M,<,>) is a scalar product space.
  4. Nov 29, 2012 #3


    Staff: Mentor

    It's usually read as "R perp".
  5. Nov 29, 2012 #4
  6. Nov 29, 2012 #5


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    Science Advisor

    If "R" is the real line, then "R perp" is a line perpendicular to it. Their direct sum is the plane containing the two lines.
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