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Basis for a matrix

  1. Feb 9, 2010 #1
    1. The problem statement, all variables and given/known data

    What is a basis for the space of 2 x 2 matrices.


    3. The attempt at a solution

    I don't understand how to this at all. Is the 2x2 identity matrix abasis for 2x2 matrices? Because it's linearly independent and spanning the space? Can anyone explain?
     
  2. jcsd
  3. Feb 9, 2010 #2

    cronxeh

    User Avatar
    Gold Member

    Yeap. Any 2x2 matrix in R^2 can be spanned by {(1,0),(0,1)} which is I2
     
  4. Feb 9, 2010 #3

    Mark44

    Staff: Mentor

    I disagree with what Cronxeh said. The space of 2x2 matrices has dimension 4, so cannot be spanned by two vectors, let alone two vectors in R2.

    The standard basis for M2,2 consists of these four matrices:
    [1 0]
    [0 0]

    [0 1]
    [0 0]

    [0 0]
    [1 0]

    [0 0]
    [0 1]
     
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