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What are the possible eigenvalues of a non-negative matrix?

Source: Brazilian Undergrad MO 2022 Problem 5

May 12, 2022
linear algebraeigenvaluesmatrixBrazilian Undergrad MO 2021

Problem Statement

Find all triplets (λ1,λ2,λ3)∈R3(\lambda_1,\lambda_2,\lambda_3) \in \mathbb{R}^3 such that there exists a matrix A3×3A_{3 \times 3} with all entries being non-negative reals whose eigenvalues are λ1,λ2,λ3\lambda_1,\lambda_2,\lambda_3.
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