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Spanning set of matrices?

  1. Apr 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Find a spanning set for the space of all 3x3 symmetric matrices.


    2. Relevant equations



    3. The attempt at a solution
    I know how to find the spanning set for vectors, but I don't know if it works the same way for matrices. Is the set's elements matrices? If so, would this be it?

    |100| |010| |001| |000| |000| |000|
    |000| |100| |000| |010| |001| |000|
    |000| |000| |100| |000| |010| |001|

    Sorry if that's messy, I'm not sure what the normal way of typing matrices is.
     
  2. jcsd
  3. Apr 19, 2009 #2
    Notice that addition and scalar multiplication for vectors and matrices are defined the same way.

    Notice also that the matrix | 1 4 |
    | 3 7 |
    (an array of numbers, a "list")
    can be represented as <1 ,4, 3, 7> (a list) which is a vector.
     
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