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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 2004-September 2005, Postdoctoral researcher at the Hamilton Institute, NUI Maynooth, Ireland
  • October 2005-August 2007, Postdoctoral researcher at University College Dublin, Ireland
  • September 2007-Present, 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 , 22-JUN-14 - 28-JUN-14.
Smigoc, H. (2014) [Conference Organising Committee Member], The 19th International Linear Algebra Society Conference, Seoul, Korea , 06-AUG-14 - 09-AUG-14.
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 , 04-JUN-14 - 12-JUN-14.
Helena Smigoc (2015) Positive coefficients of power series related to the spectral gap. [Oral Presentation], Mat Triad 2015, Coimbra, Portugal , 07-SEP-15 - 11-SEP-15.
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 , 05-AUG-08 - 07-AUG-08.
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 , 16-JUN-08 - 18-JUN-08.
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 , 27-FEB-08 - 29-FEB-08.
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 , 21-JUN-10 - 25-JUN-10.
Helena Smigoc; (2010) Nonnegative realization of spectra with two positive eigenvalues. [Invited Oral Presentation], Workshop on Nonnegative Matrices and Related Topics 2, Segovia, Spain , 12-JUL-10 - 14-JUL-11.
Helena Smigoc; (2011) Symmetric Nonnegative Inverse Eigenvalue Problem. [Invited Lecture], Workshop on Linear Algebra and Applications, Maynooth, Ireland , 17-OCT-11 - 17-OCT-11.
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 , 02-SEP-12 - 04-SEP-13.
Smigoc, H (2012) Constructive approach to the nonnegative inverse eigenvalue problem. [Invited Lecture], 2012 Haifa Matrix Theory conference, Haifa, Israel , 12-NOV-12 - 15-NOV-13.
Smigoc, H (2012) Companion type matrices in the nonnegative inverse eigenvalue problem. [Oral Presentation], 1-st Irish Linear Algebra and Matrix Theory Meeting, Galway, Ireland , 08-DEC-12 - 08-DEC-12.
Smigoc, H (2013) Patterns of symmetric matrices that allow the characteristic polynomial to be a square. [Invited Lecture], Irish Mathematical Society Meeting, Maynooth, Ireland , 26-AUG-13 - 27-AUG-13.
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 , 03-JUN-13 - 07-JUL-13.
'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.; (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.; (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.
               

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.93-106 [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 :1053-1069. [DOI] [Details]
Borobia, A,Canogar, R,Smigoc, H; (2010) 'A matrix completion problem over integral domains: the case with 2n-3 prescribed entries'. Linear Algebra and Its Applications, 433 :606-617. [DOI] [Details]
Ellard, R.; Smigoc, H. (2016) 'Connecting sufficient conditions for the Symmetric Nonnegative Inverse Eigenvalue Problem'. Linear Algebra and Its Applications, 498 (1):521-552. [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 :48-70. [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 (1-2):687-707. [DOI] [Details]
Ellard, R.; Smigoc, H. (2014) 'Constructing new realisable lists from old in the NIEP'. Linear Algebra and Its Applications, 440 (1):218-232. [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 :378-393. [DOI] [Details]
Oblak, P; Smigoc, H (2014) 'Graphs that allow all the eigenvalue multiplicities to be even'. Linear Algebra and Its Applications, 454 (1):72-90. Available Online [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):215-233. Available Online [DOI] [Details]
Smigoc, Helena; (2004) 'The inverse eigenvalue problem for nonnegative matrices'. Linear Algebra and Its Applications, 393 :365-374. [DOI] [Details]
Smigoc, Helena; (2005) 'Construction of nonnegative matrices and the inverse eigenvalue problem'. Linear and Multilinear Algebra, 53 (2):85-96. [DOI] [Details]
Laffey, TJ, Smigoc, H, ; (2007) 'Construction of nonnegative symmetric matrices with given spectrum'. Linear Algebra and Its Applications, 421 :97-109. [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 :672-685. [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 :609-624. [DOI] [Details]
Laffey, TJ,Smigoc, H; (2008) 'On a classic example in the nonnegative inverse eigenvalue problem'. Electronic Journal of Linear Algebra, 17 :333-342. [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):2017-2028. [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):629-649. Available Online [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 (1-2):228-240. Available Online [Details]
Laffey, TJ; Smigoc, H (2013) 'Simultaneous reduction of matrices in the presence of a nonderogatory matrix'. Linear Algebra and Its Applications, 438 :3885-3890. [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 :3719-3722. [DOI] [Details]
Johnson, C. R. and Smigoc, H.; Yang, D.; (2014) 'Solution Theory for Systems of Bilinear Equations'. Linear and Multilinear Algebra, 62 (12):1553-1566. [DOI] [Details]
T. J. Liffey; H. Smigoc; (2006) 'Nonnegative realization of spectra having negative real parts'. Linear Algebra and Its Applications, 416 :148-159. [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:   
  • Spectral Properties of Nonnegative Matrices
  • Sign patterns of coefficients of power series
  • Spectral Graph Theory
  • Algebra Lengths 
  • Simultaneous Reduction of Matrices 
  • Common Solution to the Lyapunov Equation
     

Collaborators

Internal Collaborators

  • Prof. Thomas J. Laffey

External Collaborators

  • Alberto Borobia
  • Roberto Canogar
  • Prof. Charles R. Johnson
  • Prof. Raphael Loewy
  • Olga Markova
  • Polona Oblak
  • Aljosa Peperko
  • Boris Zaslavsky
  • Dian Yang