The Real and the Symmetric Nonnegative Inverse Eigenvalue Problems Are Different
نویسندگان
چکیده
We show that there exist real numbers λ1, λ2, . . . , λn that occur as the eigenvalues of an entry-wise nonnegative n-by-n matrix but do not occur as the eigenvalues of a symmetric nonnegative n-by-n matrix. This solves a problem posed by Boyle and Handelman, Hershkowitz, and others. In the process, recent work by Boyle and Handelman that solves the nonnegative inverse eigenvalue problem by appending 0’s to given spectral data is refined.
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