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Copyright © 2019 H. Pickmann-Soto et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We consider the following inverse extreme eigenvalue problem: given the real numbers {λ(j) 1 , λ(j) j }nj=1 and the real vector x = (x1, x2, . . . , xn), to construct a nonsymmetric tridiagonal matrix and a nonsymmetric arrow matrix such that {λ(j) 1 , λ(j) j }nj=1 are the minimal and the maximal eigenvalues of each one of their leading principal submatrices, and (x(n), λ(n) n ) is an eigenpair of the matrix. We give sufficient conditions for the existence of suchmatrices. Moreover our results generate an algorithmic procedure to compute a unique solution matrix.

Extreme Spectra Realization by Nonsymmetric Tridiagonal and Nonsymmetric Arrow Matrices