Construction of nonnegative symmetric matrices with given spectrum

Abstract Let σ  = ( λ 1 , … ,  λ n ) be the spectrum of a nonnegative symmetric matrix A with the Perron eigenvalue λ 1 , a diagonal entry c and let τ  = ( μ 1 , … ,  μ m ) be the spectrum of a nonnegative symmetric matrix B with the Perron eigenvalue μ 1 . We show how to construct a nonnegative symmetric matrix C with the spectrum ( λ 1 + max { 0 , μ 1 - c } , λ 2 , … , λ n , μ 2 , … , μ m ) .

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