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Range of spectral radius

Source: 2018 South Korea USCM P5

August 14, 2020
linear algebramatrixspectrumcollege contests

Problem Statement

A real symmetric 2018×20182018\times 2018 matrix A=(aij)A=(a_{ij}) satisfies ∣aij−2018∣≤1|a_{ij}-2018|\leq 1 for every 1≤i,j≤20181\leq i,j\leq 2018. Denote the largest eigenvalue of AA by λ(A)\lambda(A). Find maximum and minumum value of λ(A)\lambda(A).
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