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Math Help - matrix powers

  1. #1
    Junior Member
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    matrix powers

    Hi,

    If I am given an nxn matrix A and the characteristic polynomial of A is (X-6)^n for A. Is there anyway to work out which of the factors is the minimum polynomial for A by DIRECTLY raising the matrix (A-XIn) to the various powers of the factors (rather than calculating the powers the long way!).

    Thanks.
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  2. #2
    Super Member Rebesques's Avatar
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    Let's see if i understand. You wish to find the minimum polynomial without effort?

    I don't think there is a royal path here. You have to find (A-6I)^2, (A-6I)^3,... until you get a zero.
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