## Algebraic Number is an Eigenvalue of Matrix with Rational Entries

## Problem 88

A complex number $z$ is called * algebraic number* (respectively,

*) if $z$ is a root of a monic polynomial with rational (respectively, integer) coefficients.*

**algebraic integer**Prove that $z \in \C$ is an algebraic number (resp. algebraic integer) if and only if $z$ is an eigenvalue of a matrix with rational (resp. integer) entries.

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