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Linear algebra questions

  1. Apr 13, 2005 #1
    I was able to show that the set of all 2x2 "symmetric" matrices is a subspace of Mat2x2(lR) using the 3 axioms. However, I wasn't able to do the same with skew-symmetric (A^T=-A). anyone can help? Thanks.
  2. jcsd
  3. Apr 14, 2005 #2


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    There's reason you can't! If A is the matrix with entries [0 1] and [-1 0] it is skew symmetric. What is A2?
  4. Apr 14, 2005 #3

    matt grime

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    Subspace, Halls, squaring it doesn't matter.


    If A^t =-A, then (kA)^t = -kA, for k a scalar

    (A+B)^t = A^t+B^t, so if they're skew symmetric then this is -A-B = -(A+B)

    so where did you proof go wrong?
  5. Apr 14, 2005 #4


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    the kernel of any linear map is a subspace.

    consider the map taking A to (A + A^t). for symetric ones consider A goes to (A-A^t).
  6. Apr 14, 2005 #5
    thanks for the help guys.
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