## What does A^(⊥) mean?

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)?

Thanks

 Blog Entries: 9 Recognitions: Homework Help Science Advisor The upside down capital T means , 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, = 0, where (M,<,>) is a scalar product space.

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 Quote by MikeyW I'm looking at a condition in a maths paper that I don't understand, essentially it is: x ∈ R ⊕ R⊥
It's usually read as "R perp".

## What does A^(⊥) mean?

The "oplus" is a direct sum. x belonging to the direct sum means that x can be uniquely written as a sum
x = a+b, where a belongs to R and b belongs to R perp.

http://en.wikipedia.org/wiki/Direct_sum_of_modules

 Recognitions: Gold Member Science Advisor Staff Emeritus 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.