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Math Help - Find an invertible matrix P

  1. #1
    Senior Member
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    Find an invertible matrix P

    Let T:R^4 --> R^4 be a linear transformation T(v) = Av where A =

    [1 1 3 1]
    [0 2 2 4]
    [0 0 3 2]
    [0 0 1 4]

    Find the characteristic polynomial of A and compute the eigenvalues of T. Find a basis for each eigenspace. Either find an invertible matrix P and a disgonal matrix D such that P^{-1}AP = D or else explain why this is impossible.



    I know how to find the characteristic polynomial and the eigenvalues of A but not T.
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  2. #2
    Junior Member nimon's Avatar
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    The eigenvalues of A are exactly the eigenvalues of T. Indeed, if T(v) = Av =\lambda v then T(v) = \lambda v.
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