Minimal Polynomial of Companion Matrix equals that Polynomial

Definition

Let $P$ be the polynomial of degree $n$ presented in the form:

$\map P x = x^n - a_{n - 1} x^{n - 1} - \cdots - a_1 x - a_0$

Let $C$ be the companion matrix of $P$.

The minimal polynomial of $C$ equals $\map P x$.


Proof


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Sources

  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): companion matrix
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