# Questions tagged [companion-matrices]

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### Companion matrix must have one Jordan block per eigenvalue: recurrence sequence perspective

Please let me know if anything is unclear in my post, as it is not recieving any responses yet, I would provide additional explanation if needed. Also if you have any idea for my problem below please ...
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### When are almost block companion matrices which yield a given characteristic polynomial connected?

This is motivated by this question Are matrices which yield a given characteristic polynomial and have specified structure connected? Let $\mathcal E \in M_n(\mathbb R)$ be a subset with following ...
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### Does every polynomial with a Perron root have a primitive matrix representation?

Let $p(x)=x^6-13x^4-20x^3+x^2-x+2$ and $C$ be the companion matrix of $p(x)$. How can I find a primitive matrix similar to $C$ ? Is there a general method to transform the companion matrix with a ...
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### How to check a special form of Companion Matrix is a Primitive Matrix or not?

Definition: A non-negative matrix square $A$ is called primitive if there is a $k$ such that all the entries of $A^k$ are positive. Lemma: If the graph associated to $A$ is strongly connected and ...
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