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T invariant subspace (intro lin alg class undergrad)

  1. Aug 4, 2011 #1
    1. The problem statement, all variables and given/known data
    V=Matrix (2x2), T(A) = (0 1 ) A , and W = {A[itex]\epsilon[/itex] V: A[itex]^{}t[/itex] = A
    (1 0)


    2. Relevant equations
    So T(A) transformation, multiplies a 2x2 matix with entries 0 1 1 0 by A with A on the right side


    3. The attempt at a solution

    I said let A be any arbitrary symmetric matrix, for example a 2x2 matrix with entries
    a b b a

    (a b)
    (b a), this that matrix multiplied on the right of 0 1 1 0, = (b a)
    (a b) , also a symmetric matrix, and therefore this matrix is also an element of W, this W is a T-invariant subspace.

    but the back of the book does not say it is T-invariant

    please point out if i am making a mistake
    test tomorrow

    thanks!
     
  2. jcsd
  3. Aug 4, 2011 #2
    Remember, a symmetric matrix A satisfies [itex]A=A^T[/itex]. That places no restriction on the main diagonal entries. An arbitrary symmetric 2x2 should be of the form

    [tex] \begin{bmatrix} x & y \\ y & z \end{bmatrix} [/tex]
     
    Last edited: Aug 4, 2011
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