Various 3 × 3 nonnegative matrices with prescribed eigenvalues and diagonal entries

In this paper, we answer the various forms of nonnegative inverse eigenvalue problems with prescribed diagonal entries for order three: real or complex general matrices, symmetric stochastic matrices, and real or complex doubly stochastic matrices. We include the known cases, the symmetric matrices...

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Veröffentlicht in:Linear algebra and its applications 2018-10, Vol.554, p.15-48
Hauptverfasser: Hwang, Jin Ok, Kim, Donggyun
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we answer the various forms of nonnegative inverse eigenvalue problems with prescribed diagonal entries for order three: real or complex general matrices, symmetric stochastic matrices, and real or complex doubly stochastic matrices. We include the known cases, the symmetric matrices and real or complex stochastic matrices, to compare the other results and for completeness. In addition, for a given list of eigenvalues, we compute the exact range for the largest value of the diagonal entries of the various nonnegative matrices.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2018.05.002