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| I have worked on several challenging problems in linear algebra and matrix theory with special emphasis on the problems connected with positivity. I made an important contribution to solving the nonnegative inverse eigenvalue problem (NIEP): characterizing the possible spectra of entrywise nonnegative matrices. The NIEP is seen as one of the central problems in matrix theory, and it has been open for over 30 years. Together with Prof. Laffey I have solved the problem when all but the dominant eigenvalue have negative real part and I have found several novel perturbation results for spectra of nonnegative matrices. In another part of my research I have been engaged in finding conditions for the existence of a common solution to the Lyapunov equation. Together with Prof. Laffey I have extended several results that were known for real matrices to the complex case. I have strong interaction with several leaders in the field. I have written several joint papers with Prof. Thomas Laffey from University College Dublin (Ireland). My other collaborators are in alphabetical order: Alberto Borobia (UNED Spain), Roberto Canogar (UNED, Spain), Prof. Charles Johnson (College of William and Mary, USA), Prof. Raphael Loewy (Technion Israel), Polona Oblak (University of Ljubljana, Slovenia). |
| T. J. Laffey and H. 'migoc; (2007) 'Structured matrices in the nonnegative inverse eigenvalue problem' In: Mathematical Papers in Honor of Eduardo Marques de Sá. Textos de Matemática, Volume 39: *. [Details] |
| T. J. Laffey and H. 'migoc,; (2007) 'Spectra of principal submatrices of nonnegative matrices'. Linear Algebra and Its Applications, . [Details] |
| T. J. Laffey and H. 'migoc, ; (2007) 'Construction of nonnegative symmetric matrices with given spectrum'. Linear Algebra and Its Applications, 421 :97-109. [Details] |
| T. J. Laffey and H. 'migoc,; (2006) 'Nonnegative realization of spectra having negative real parts'. Linear Algebra and Its Applications, 416 :148-159. [Details] |
| 'migoc, H.; (2006) Spectrum of Nonnegative Matrices. [Invited Lecture], Workshop on Nonnegative Matrices: Theory and Applications, Hamilton Institute, Maynooth, Ireland , 09-JUL-06 - 12-JUL-06. |
| Smigoc, H.; (2002) The maximal function and the Calderon-Zygmund decomposition. [N/A], TULKA Internet Seminar, Blaubeuren, Germany , 01-JUN-02 - 04-FEB-06. |
| Smigoc, H.; (2005) Necessary conditions for the existence of a common quadratic Lyapunov function. [Invited Oral Presentation], Linear Algebra Workshop 2005, Bled, Slovenia , 16-MAY-05 - 24-MAY-05. |
| 'migoc, H.; (2004) Inverse eigenvalue problem for nonnegative matrices. [Invited Oral Presentation], 11th Conference of the International Linear Algebra Society, Coimbra, Portugal , 19-JUL-04 - 22-JUL-04. |
| 'migoc, H.; (2005) Inverse eigenvalue problem for nonnegative matrices. [Plenary Lecture], MAT-TRIAD 2005, Bedlewo, Poland , 03-MAR-05 - 05-MAR-05. |
| 'migoc, H.; (2006) Perturbation results for spectra of nonnegative matrices. [Invited Oral Presentation], 13th Conference of the International Linear Algebra Society, Amsterdam , 18-JUL-06 - 21-JUL-06. | |||||||||
| Smigoc, H.; (2007) Spectrum of Nonnegative Matrices. [Oral Presentation], Robert C. Thompson Matrix Meeting 2007, Auburn University, Alabama, USA, , 24-MAR-07. | |||||||||
| 'migoc, H.; (2007) Spectra of Principal Submatrices of Nonnegative Matrices. [Invited Oral Presentation], Haifa Matrix Theory Conference 2007, Technion, Haifa, Israel , 01-APR-07. | |||||||||
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