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Found problems: 1

2018 Korea USCM, 5
Tags: matrix , linear algebra , spectrum
A real symmetric $2018\times 2018$ matrix $A=(a_{ij})$ satisfies $|a_{ij}-2018|\leq 1$ for every $1\leq i,j\leq 2018$. Denote the largest eigenvalue of $A$ by $\lambda(A)$. Find maximum and minumum value of $\lambda(A)$.