1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: What is the difference between a Cartesian Product and a Direct Sum

  1. Sep 12, 2010 #1
    1. The problem statement, all variables and given/known data
    17. Let U = f(x; y; 0) : x 2 R; y 2 Rg, E1 = f(x; 0; 0) : x 2 Rg, and E3 = f(0; 0; x) :
    x 2 Rg: Are the following assertions true or false? Explain.
    (a) U + E1 is a subspace of R3:
    (b) U  E1 is a direct sum decomposition of U + E1:
    (c) U  E3 is a direct sum decomposition of R3:

    2. Relevant equations

    3. The attempt at a solution

    I really need to know, from what my teacher told us about it, it seems like a Cartesian Product is adding dimensionality to two sets and that a Direct Sum is just adding every possible vector combination from two vector spaces together. But I really don't know
  2. jcsd
  3. Sep 14, 2010 #2
    Set A and B

    Cartesian product
    [tex]A\timesB=\left\{(a,b)|a \in A,\ b \in B\right\}[/tex]

    Direct Sum

    [tex]A+B=\left\{a+b|a \in A,\ b \in B\right\}[/tex]

    something like that ;P
  4. Sep 14, 2010 #3
    No, that's just an addition of subspaces, I'm talking about the "direct sum" its the little circle with the plus sign in it, I think its like a partisan cross product, but with vector spaces... I think
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook