Helena Smigoc
Lecturer
School of Mathematics & Statistics
Tel: (01) 716 2582
Email: helena.smigoc@ucd.ie
Biography
 PhD in Mathematics, University of Ljubljana, Slovenia
 November 2004September 2005, Postdoctoral researcher at the Hamilton Institute, NUI Maynooth, Ireland
 October 2005August 2007, Postdoctoral researcher at University College Dublin, Ireland
 September 2007Present, Lecturer at University College Dublin, Ireland
Professional
Conference Contributions
Smigoc, H (2014) From positive matrices to power series with positive coefficients. [Invited Oral Presentation], 17th Internet Seminar, The workshop, Blaubeuren, Germany , 22JUN14  28JUN14. 
Smigoc, H. (2014) [Conference Organising Committee Member], The 19th International Linear Algebra Society Conference, Seoul, Korea , 06AUG14  09AUG14. 
Smigoc, H (2014) Patterns of symmetric matrices that allow all the eigenvalue multiplicities to be even. [Oral Presentation], The Seventh Linear Algebra Workshop, Ljubljana, Slovenia , 04JUN14  12JUN14. 
Helena Smigoc (2015) Positive coefficients of power series related to the spectral gap. [Oral Presentation], Mat Triad 2015, Coimbra, Portugal , 07SEP15  11SEP15. 
H. ¿migoc; (2008) A constructive approach to the nonnegative inverse eigenvalue problem. [Invited Lecture], Hamilton Institute Workshop on Nonnegative Matrices and Related Topics, Maynooth, Ireland , 05AUG08  07AUG08. 
H. ¿migoc; (2008) An example of constructing a nonnegative matrix with given spectrum. [Invited Lecture], 15th Conference of the International Linear Algebra Society, Cancun, Mexico , 16JUN08  18JUN08. 
H. ¿migoc; (2008) The effect of adding zeros to the spectrum in the nonnegative inverse eigenvalue problem. [Invited Lecture], Workshop on Nonnegative Matrices and Related Topics, San Pedro de Atacama, Chile , 27FEB08  29FEB08. 
Helena Smigoc; (2010) Some constructive methods in the symmetric nonnegative inverse eigenvalue problem. [Invited Oral Presentation], 16th Conference of the International Linear Algebra Society, PIsa, Italy , 21JUN10  25JUN10. 
Helena Smigoc; (2010) Nonnegative realization of spectra with two positive eigenvalues. [Invited Oral Presentation], Workshop on Nonnegative Matrices and Related Topics 2, Segovia, Spain , 12JUL10  14JUL11. 
Helena Smigoc; (2011) Symmetric Nonnegative Inverse Eigenvalue Problem. [Invited Lecture], Workshop on Linear Algebra and Applications, Maynooth, Ireland , 17OCT11  17OCT11. 
Smigoc, H (2012) Power series with positive coefficients in the context of the nonnegative inverse eigenvalue problem. [Oral Presentation], The 4th International Symposium on Positive Systems, Maynooth, Ireland , 02SEP12  04SEP13. 
Smigoc, H (2012) Constructive approach to the nonnegative inverse eigenvalue problem. [Invited Lecture], 2012 Haifa Matrix Theory conference, Haifa, Israel , 12NOV12  15NOV13. 
Smigoc, H (2012) Companion type matrices in the nonnegative inverse eigenvalue problem. [Oral Presentation], 1st Irish Linear Algebra and Matrix Theory Meeting, Galway, Ireland , 08DEC12  08DEC12. 
Smigoc, H (2013) Patterns of symmetric matrices that allow the characteristic polynomial to be a square. [Invited Lecture], Irish Mathematical Society Meeting, Maynooth, Ireland , 26AUG13  27AUG13. 
Smigoc, H (2013) Constructing new spectra of nonnegative matrices from known spec tra of nonnegative matrices. [Invited Lecture], International Linear Algebra Society Meeting, Providence, RI, USA , 03JUN13  07JUL13. 
'migoc, H.; (2006) Spectrum of Nonnegative Matrices. [Invited Lecture], Workshop on Nonnegative Matrices: Theory and Applications, Hamilton Institute, Maynooth, Ireland , 09JUL06  12JUL06. 
Smigoc, H.; (2005) Necessary conditions for the existence of a common quadratic Lyapunov function. [Invited Oral Presentation], Linear Algebra Workshop 2005, Bled, Slovenia , 16MAY05  24MAY05. 
'migoc, H.; (2005) Inverse eigenvalue problem for nonnegative matrices. [Plenary Lecture], MATTRIAD 2005, Bedlewo, Poland , 03MAR05  05MAR05. 
'migoc, H.; (2006) Perturbation results for spectra of nonnegative matrices. [Invited Oral Presentation], 13th Conference of the International Linear Algebra Society, Amsterdam , 18JUL06  21JUL06. 
Smigoc, H.; (2007) Spectrum of Nonnegative Matrices. [Oral Presentation], Robert C. Thompson Matrix Meeting 2007, Auburn University, Alabama, USA, , 24MAR07. 
'migoc, H.; (2007) Spectra of Principal Submatrices of Nonnegative Matrices. [Invited Oral Presentation], Haifa Matrix Theory Conference 2007, Technion, Haifa, Israel , 01APR07. 
Publications
Book Chapters
Laffey T.J.; Smigoc, H.; (2007) 'Structured matrices in the nonnegative inverse eigenvalue problem' In: O. Azenhas; A. L. Duarte; J. F. Queiró; A. P. Santana (eds). Mathematical Papers in Honor of Eduardo Marques de Sá. Portugal: Textos de Matemática, Volume 39. , pp.93106 [Details] 
Peer Reviewed Journals
T. J. Laffey and H. 'migoc,; (2008) 'Spectra of principal submatrices of nonnegative matrices'. Linear Algebra and Its Applications, . [DOI] [Details] 
Laffey, TJ,Smigoc, H; (2010) 'Nonnegatively realizable spectra with two positive eigenvalues'. Linear and Multilinear Algebra, 58 :10531069. [DOI] [Details] 
Borobia, A,Canogar, R,Smigoc, H; (2010) 'A matrix completion problem over integral domains: the case with 2n3 prescribed entries'. Linear Algebra and Its Applications, 433 :606617. [DOI] [Details] 
Ellard, R.; Smigoc, H. (2016) 'Connecting sufficient conditions for the Symmetric Nonnegative Inverse Eigenvalue Problem'. Linear Algebra and Its Applications, 498 (1):521552. [DOI] [Details] 
Oblak,P.; Smigoc, H. (2017) 'The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph'. Linear Algebra and Its Applications, 512 :4870. [DOI] [Details] 
Thomas Laffey, Raphael Loewy, Helena Smigoc (2016) 'Power series with positive coefficients arising from the characteristic polynomials of positive matrices'. Mathematische Annalen, 364 (12):687707. [DOI] [Details] 
Ellard, R.; Smigoc, H. (2014) 'Constructing new realisable lists from old in the NIEP'. Linear Algebra and Its Applications, 440 (1):218232. [DOI] [Details] 
Liffey, T; Markova, O; Smigoc, H (2016) 'The effect of assuming the identity as a generator on the length of the matrix algebra'. Linear Algebra and Its Applications, 498 :378393. [DOI] [Details] 
Oblak, P; Smigoc, H (2014) 'Graphs that allow all the eigenvalue multiplicities to be even'. Linear Algebra and Its Applications, 454 (1):7290. [DOI] [Details] 
Borobia, A.; Canogar, R.; Smigoc, H. (2014) 'A matrix completion problem over integral domains: the case with 2n−3 prescribed blocks'. Proyecciones Journal of Mathematics, 33 (2):215233. [DOI] [Details] 
Smigoc, Helena; (2004) 'The inverse eigenvalue problem for nonnegative matrices'. Linear Algebra and Its Applications, 393 :365374. [DOI] [Details] 
Smigoc, Helena; (2005) 'Construction of nonnegative matrices and the inverse eigenvalue problem'. Linear and Multilinear Algebra, 53 (2):8596. [DOI] [Details] 
Laffey, TJ, Smigoc, H, ; (2007) 'Construction of nonnegative symmetric matrices with given spectrum'. Linear Algebra and Its Applications, 421 :97109. [DOI] [Details] 
Laffey, TJ; Smigoc, H; (2007) 'Tensor conditions for the existence of a common solution to the Lyapunov equation'. Linear Algebra and Its Applications, 420 :672685. [DOI] [Details] 
Laffey, TJ; Smigoc, H; (2007) 'Common solution to the Lyapunov equation for 2 x 2 complex matrices'. Linear Algebra and Its Applications, 420 :609624. [DOI] [Details] 
Laffey, TJ,Smigoc, H; (2008) 'On a classic example in the nonnegative inverse eigenvalue problem'. Electronic Journal of Linear Algebra, 17 :333342. [DOI] [Details] 
Laffey, Thomas J. and Smigoc, Helena; (2010) 'Sufficient conditions on commutators for a pair of stable matrices to have a common solution to the Lyapunov equation'. SIAM Journal on Matrix Analysis and Applications, 31 (4):20172028. [DOI] [Details] 
Laffey, T. J. and Loewy, R. and ¿migoc, H.; (2009) 'Nonnegative matrices that are similar to positive matrices'. SIAM Journal on Matrix Analysis and Applications, 31 (2):629649. [Details] 
Laffey, T. J. and ¿migoc, H.; (2009) 'Common Lyapunov solutions for two matrices whose difference has rank one'. Linear Algebra and Its Applications, 431 (12):228240. [Details] 
Laffey, TJ; Smigoc, H (2013) 'Simultaneous reduction of matrices in the presence of a nonderogatory matrix'. Linear Algebra and Its Applications, 438 :38853890. [DOI] [Details] 
Johnson, CR,Smigoc, H (2013) 'A matricial proof of the symmetric exchange axiom for eigenvalues of principal submatrices of a complex Hermitian matrix'. Linear Algebra and Its Applications, 438 :37193722. [DOI] [Details] 
Johnson, C. R. and Smigoc, H.; Yang, D.; (2014) 'Solution Theory for Systems of Bilinear Equations'. Linear and Multilinear Algebra, 62 (12):15531566. [DOI] [Details] 
T. J. Liffey; H. Smigoc; (2006) 'Nonnegative realization of spectra having negative real parts'. Linear Algebra and Its Applications, 416 :148159. [DOI] [Details] 
Conference Publications
O'Hagan, A; Cutajar, S; Smigoc, H (2016) Actuarial Risk Matrices: the Nearest Positive Semidefinite Matrix Problem Actuarial Teachers and Researchers' Conference [Details] 
Research
Research Interests
My research research interests are in areas of linear algebra, matrix theory and combinatorics. The heart of my research is the nonnegative inverse eigenvalue problem (NIEP), a problem that seen as one of the most difficult and intriguing open problems in matrix theory today. Starting with the NIEP my research interests broadened to several aspects of matrix theory with special emphasis on the problems that are in some way connected with positivity. My work on the questions about the sign patterns of coefficients of polynomials and power series brought my research interest outside the scope of matrix theory. While I am not working directly on real world applications, my work is closely connected with applications is several areas that range from finance to science and engineering. Below I list main research topics that I am working on:

Teaching
Collaborators
Internal Collaborators

External Collaborators
