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Math Help - Similiar matrix to a given one using Primary Decomposition Theorem

  1. #1
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    Similiar matrix to a given one using Primary Decomposition Theorem

    Let A be a 3x3 real matriz. Let $$m(x)=(x-c)(x{^2}+ax+b)$$ be A`s minimal polynomial such that cannot be written in linear factors. Prove A is similar to

    $$\[ \left( \begin{array}{ccc}<br />
0 & -b & 0 \\<br />
1 & -a & 0 \\<br />
0 & 0 & c \end{array} \right)\$$
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  2. #2
    Super Member Rebesques's Avatar
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    Re: Similiar matrix to a given one using Primary Decomposition Theorem

    Well, if the given matrix is called B, then det(B-xI)=m(x), and since this has no linear factors,
    m is also the minimal polynomial for B, so...
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