# Thread: Similiar matrix to a given one using Primary Decomposition Theorem

1. ## 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}
0 & -b & 0 \\
1 & -a & 0 \\
0 & 0 & c \end{array} \right)\$

2. ## 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...