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Showing a set of matrices is a group

  1. Feb 12, 2010 #1
    1. The problem statement, all variables and given/known data
    show the set of nxn diagonal matrices is a group under matrix addition


    2. Relevant equations



    3. The attempt at a solution
    it doesn't say what set the entries are from, so i'm assuming it's reals.
    so i need to show that there is closure, it's associative, there's an identity element, and there's an inverse. i know that there's an identity element, the matrix with just zeroes, and i know the inverse is just -A for matrix A. it's addition, so i know that it's associative, and in my head i can tell that there is closure.
    my main problem is notation. how to do i actually express this? i.e., what's the general notation for a nxn matrix?
     
  2. jcsd
  3. Feb 13, 2010 #2
    Here is a general diagonal nxn matrix:

    [tex]\left( \begin{array}{c c c c} x_1 & & & \\ & x_2 & & \\ & & ... & \\ & & & x_n \end{array} \right)[/tex]

    Alternatively, you can say "let A be a diagonal nxn matrix" and index the entries with [itex]A_{ij}[/itex].
     
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