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What does R^(n x m) mean?

  1. Oct 24, 2011 #1
    1. The problem statement, all variables and given/known data

    So yeah as the topic says. What does R^(nxm) mean? Is that a matrix or an n x m space. The notation is really confusing and sometimes it means something else.

    I'm doing regression analysis right now and this shows up a lot. Is it a matrix when you say something like C = ℝ^(k x m). I'm not sure if that means its a k x m matrix or a k x m space. Mainly because in examples when they say that, it shows up as a k x m matrix. I'm guessing its a a matrix because of the = sign? If you had an E sign instead it would be contained in a space?



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 24, 2011 #2

    Mark44

    Staff: Mentor

    It's the vector space of n X m matrices, with real entries.
     
  4. Oct 24, 2011 #3
    Thanks! That cleared up so much...

    Another quick question if you may know.

    If i have the observations. (xi1,...xik,yi1,....,yim). If i set X = (xij) and Y = (yij). What are those? Is that an i x k matrix for X and an i x m matrix for Y?
     
  5. Oct 24, 2011 #4

    Mark44

    Staff: Mentor

    xi1,...xik would be the i-th row of a matrix with k columns.
    yi1,....,yim would be the i-th row of a matrix with m columns.
    That notation is usually used for matrices, where xij represents an arbitrary element of the matrix. Same for yij.
    Probably not i x k and i x m, but <something> x k and <something> by m. I can't tell from what you have here.
     
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