Eigenvalues of Companion Matrix are Zeroes of 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 eigenvalues of $C$ are the zeroes of $P$.

Proof

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Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): companion matrix