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Brazil Undergrad MO
2021 Brazil Undergrad MO
Problem 5
Problem 5
Part of
2021 Brazil Undergrad MO
Problems
(1)
What are the possible eigenvalues of a non-negative matrix?
Source: Brazilian Undergrad MO 2022 Problem 5
5/12/2022
Find all triplets
(
λ
1
,
λ
2
,
λ
3
)
∈
R
3
(\lambda_1,\lambda_2,\lambda_3) \in \mathbb{R}^3
(
λ
1
,
λ
2
,
λ
3
)
∈
R
3
such that there exists a matrix
A
3
×
3
A_{3 \times 3}
A
3
×
3
with all entries being non-negative reals whose eigenvalues are
λ
1
,
λ
2
,
λ
3
\lambda_1,\lambda_2,\lambda_3
λ
1
,
λ
2
,
λ
3
.
linear algebra
eigenvalues
matrix
Brazilian Undergrad MO 2021