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Math Help - Jordan form

  1. #1
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    Jordan form

    Would you help me with this:

    Let A is in C^4. A =
    ( 0 0 0 -1
    1 0 0 2
    0 1 0 -2
    0 0 1 2)

    (i)Determine the minimal characteristic polynomials of A.
    (ii) Determine the Jordan form of A.
    (iii) Construct a basis B of C^4 such that [T_A]_B is in Jordan form , where T_A is the linear map T_A: -> C4 : X -> AX.

    Thank you!
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  2. #2
    Member
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    Thanks
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    Start by computing the eigenvalues from the c_A(x) and then the eigenvectors.. put the eigenvectors in diagonalizable form P such that P^-1AP= D which is your jordan block form. The new basis B will just be the basis of eigenspaces.
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