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Michael Tsatsomeros
(Μιχάλης Τσατσóμοιρος)
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Office: Neill Hall 229
Phone: +1-509-335-3144
Email: tsat at wsu dot edu
Curriculum Vitae
Curriculum Vitae
Education
Education
Ph.D., Mathematics, University of Connecticut - 1990
Supervisor: Michael Neumann (In Memoriam)M.Sc., Mathematics, Concordia University, Montreal - 1986
Supervisor: Ronald J. Stern - Here's a copy of my thesisDiploma, Mathematics, University of Patras, Greece - 1984
Research Interests
Research Interests
Linear algebra, matrix analysis, especially the theory of nonnegative matrices and their generalizations. Particular interests include the numerical range; graphs and patterns associated with matrices; numerical linear algebra; applications in dynamical systems, control theory, data analysis, machine learning and artificial intelligence.
Work Experience
Work Experience
2007 - present, Professor, Washington State University, Pullman, WA
2019-21 SPARC Visiting Faculty, Indian Institute of Technology - Madras, India
2001-07, Associate Professor, Washington State University
1997-2002, Associate Professor, University of Regina, Saskatchewan, Canada
1994-97, Assistant Professor, University of Regina
1993-94, Adjunct Assistant Professor, University of Regina
1993, Visiting Assistant Professor, College of William and Mary, Williamsburg, VA
1992, Visiting Assistant Professor, University of Wisconsin, Madison, WI
1990-92, Post-doctoral Fellow, University of Victoria, British Columbia, Canada
Supervision
Supervision
Current graduate students
Current graduate students
Ben Clark, Allison Roberson, Collin Parker, Eleni Boutsika
Completed Ph.D. students
Completed Ph.D. students
Seong Park (Ph.D., 2025)
Thesis title: Factorizations of Copositive Matrices and the Copositive Range
Samir Mondal (co-Chair with K.C. Sivakumar, Ph.D., IIT Madras, 2024)
Thesis title: Exploring Matrix Positivity Classes: Properties and ApplicationsWail Alahmadi (Ph.D., 2023)
Thesis tittle: Convex Sets of Stable MatricesSushmitha Parameswaran (co-Chair with K.C. Sivakumar, Ph.D., IIT Madras, 2021)
Thesis title: On Some Generalizations of the Class of Q-MatricesHung Le (Ph.D., 2020)
Thesis title: Matrix Analysis Primer for Inhomogeneous Markov ChainsFaith Zhang (Ph.D., 2020)
Thesis title: Rank One Perturbations and ApplicationsMegan Wendler (Ph.D., 2020)
Thesis title: Semimonotone MatricesPatrick Torres (Ph.D., 2018)
Thesis title: Stability Analysis, Convex Hulls of Matrix Powers and Their Relations to P-matricesMichael Kasigwa (Ph.D., 2017)
Thesis title: Eventual Cone InvarianceThomas Cameron (Ph.D., 2016)
Thesis title: On the Computation of Eigenvalues, Spectral Bounds and Hessenberg Form of Matrix PolynomialsPietro Paparella (Ph.D., 2013, co-supervised with J.J. McDonald)
Thesis title: Matrix Roots of Nonnegative and Eventually Nonnegative MatricesJimmy Burk (Ph.D., 2012)
Thesis title: Eigenspaces of Tournament MatricesKent Griffin (Ph.D., 2006)
Thesis title: Solving the Principal Minor Assignment Problem and Related ComputationsBishan Li (Ph.D., Univ. of Regina, 1998)
Thesis title: Generalizations of Diagonal Dominance in Matrix Theory
Post-Doctoral Fellows
Post-Doctoral Fellows
Fei Zhou (Post-doctoral fellow, 2006)
Panos Psarrakos (Post-doctoral fellow, 2000)
Currently: Professor, Mathematics, National Technical University of AthensMark Krupnik (Post-doctoral fellow, 1994-1995)
Currently: Retalon, Inc (inventory management and forecasting tools), Co-founder and President
Completed Master's Students
Completed Master's Students
Allison Roberson (M.Sc., 2024), Kenny Nguyen (M.Sc., 2021), Zahra Al Dushaishi (M.Sc., 2019), Dillon Gibblin (M.Sc., 2014), Thomas Cameron (M.Sc., 2013), Dan Hooper (M.Sc., 2013), Giang Trinh (M.Sc., 2010), Lisa Ellison (M.Sc., 2008), Chris Kanyer (M.Sc., 2006), Olga Slyusareva (M.Sc., 2005), Nelson Phouphakone (M.Sc., 2005), Rokas Varaneckas (M.Sc., 2004), Pietro Paparella (M.Sc., 2003)
Grants/Awards
Grants/Awards
Tom & Julie Lutz Science and Math Teaching Excellence, College of Arts and Sciences, WSU, 2024
Excellence in Graduate Advising and Mentoring, College of Arts and Sciences, WSU, 2021
SPARC Indian Institure of Technology-Madras Collaboration Grant, 2019-2021
Outstanding Research Award, Mathematics, WSU, 2007
Catalyzing the Future Award, WSU, 2003
NSERC Research Grants: 1994-1997, 1997-2001, 2001-2002
NSERC Equipment Grants: 1994, 1996, 2001
Merit Awards, Univ. of Regina, 1996, 1999
Books
Books
Panayiotis J. Psarrakos and Michael J. Tsatsomeros.
Linear Algebra and Matrix Methods, First Edition, Cognella, San Diego, 2024.Charles R. Johnson, Ronald L. Smith, and Michael J. Tsatsomeros.
Matrix Positivity. Cambridge University Press, 2020.
Publications/(P)reprints
Publications/(P)reprints
Aik. Aretaki, M. Adam, and M. Tsatsomeros.
Curves and Spectrum Localization for Real Matrices.
Linear Algebra and its Applications, 733:116-154, 2026.Seong Park, Nurhan Colatoglou, Michael Tsatsomeros.
Electronic Journal of Linear Algebra, 41:575-587, 2025.
Tikesh Verma, Debasisha Mishra, Michael Tsatsomeros.
Cayley Transform for Toeplitz and Dual Matrices.
Linear Algebra and its Applications, 703:627-644, 2024.
M.J. Tsatsomeros, D.D. Olesky, P. van den Driessche.
Characterizations of Complex P-matrices.
Electronic Journal of Linear Algebra, 40:682-691, 2024.
Samir Mondal, K.C. Sivakumar, and M.J. Tsatsomeros.
P-matrix Powers.
Linear Algebra and its Applications, 699:355-366, 2024.Samir Mondal, K.C. Sivakumar, and M.J. Tsatsomeros.
The Cayley Transform of Prevalent Matrix Classes.
Linear Algebra and its Applications, 681:1-20, 2024.Samir Mondal, K.C. Sivakumar, and M.J. Tsatsomeros.
New Results on M-matrices, H-matrices and their Inverse Classes.
Electronic Journal of Linear Algebra, 38:729-744, 2022.Hung V. Le and M.J. Tsatsomeros
Matrix Analysis for Continuous-Time Markov Chains.
Special Matrices, 10:219-233, 2022.Michael J. Tsatsomeros and Yueqiao Faith Zhang.
Recursive Rank One Perturbations for Pole Placement and Cone Reachability.
Applied Mathematics and Computation, Vol. 416, Issue C, March 2022.K.C. Sivakumar, P. Sushmitha, and M.J. Tsatsomeros.
Q#-Matrices and Q†-Matrices: Two Extensions of the Q-Matrix Concept.
Linear and Multilinear Algebra, 70(21):6947-6964, 2022.Michael J. Tsatsomeros and Yueqiao Faith Zhang.
The Fiber of P-matrices: The Recursive Construction of All Matrices with Positive Principal Minors.
Linear and Multilinear Algebra, 69:224-232, 2021.J.J. McDonald, R. Nandi, K.C. Sivakumar, P. Sushmitha, M.J. Tsatsomeros, Enzo Wendler, and Megan Wendler.
M-matrix and Inverse M-matrix Extensions.
Special Matrices, 8:186-203, 2020.Charles R. Johnson, Ronald L. Smith, and Michael J. Tsatsomeros.
Matrix Positivity. Cambridge University Press, 2020.Projesh Nath Choudhury and Michael J. Tsatsomeros.
Algorithmic Detection and Construction of N-matrices.
Linear Algebra and Its Applications, 602:46-56, 2020.Michael J. Tsatsomeros and Megan Wendler.
Semimonotone Matrices.
Linear Algebra and Its Applications, 578:207-224, 2019.P.K. Torres and M.J. Tsatsomeros.
Stability and Convex Hulls of Matrix Powers.
Linear and Multilinear Algebra, 66(4):769-775, 2018.K.C. Sivakumar and M.J. Tsatsomeros.
Semipositive Matrices and Their Semipositive Cones.
Positivity, 22(1):379-398, 2018.Ik-Pyo Kim and M.J. Tsatsomeros.
Inverse Relations in Shapiro's Open Questions
Discrete Mathematics, 341:691-700, 2018.Ik-Pyo Kim and M.J. Tsatsomeros.
Pascal Eigenspaces and Invariant Sequences of the First or Second Kind.
Linear Algebra and its Applications, 535:171-190, 2017.Aik. Aretaki, P. Psarrakos, and M. Tsatsomeros.
The Envelope of Tridiagonal Toeplitz Matrices and Block-Shift Matrices.
Linear Algebra and its Applications, 532:60-85, 2017.M. Kasigwa and M.J. Tsatsomeros.
Eventual Cone Invariance.
Electronic Journal of Linear Algebra, 32:204-216, 2017.M.J. Tsatsomeros.
Geometric Mapping Properties of Semipositive Matrices.
Linear Algebra and its Applications, 498:349-359, 2016.P. Psarrakos and M.J. Tsatsomeros.
On the Geometry of the Envelope of a Matrix.
Applied Mathematics and Computation, 244:132-141, 2014.J.J. McDonald, P. Paparella, and M.J. Tsatsomeros.
Matrix Roots of Eventually Positive Matrices.
Linear Algebra and its Applications, 456:122-137, 2014.M. Cavers, S.M. Cioaba, S. Fallat, D.A. Gregory, W. Haemers, S.J. Kirkland, J.J. McDonald, and M. Tsatsomeros.
Skew-Adjency Matrices of Graphs.
Linear Algebra and its Applications, 436:512-4529, 2012.D.D. Olesky, M.J. Tsatsomeros, and P. van den Driessche.
Sign Patterns with a Nest of Positive Principal Minors.
Linear Algebra and its Applications, 436:4392-4399, 2012.J. Burk and M.J. Tsatsomeros.
On the Brualdi-Li Matrix and its Perron Eigenspace.
Electronic Journal of Linear Algebra, 23:212-230, 2012.P. Psarrakos and M.J. Tsatsomeros.
An Envelope for the Spectrum of a Matrix.
Central European Journal of Mathematics, 10:292-302, 2012.Michael Tsatsomeros.
In Memoriam: Michael (Miki) Neumann (1946-2011).
Linear Algebra and its Applications, 436:1-11, 2012.George Psarrakos and Michael Tsatsomeros.
Ratio Monotonicity for Tail Probabilities in the Renewal Risk Model.
Probability in the Engineering and Informational Sciences., 25:171-185, 2011.A. Berman, M. Catral, L.M. DeAlba, A. Elhashash, F.J. Hall, L. Hogben, I.-J. Kim, D.D. Olesky, P. Tarazaga, M.J. Tsatsomeros, and P. van den Driessche.
Sign Patterns that Allow Eventual Positivity.
Electronic Journal of Linear Algebra, 19:108-120, 2009/2010.E. Ellison, L. Hogben, and M. Tsatsomeros.
Sign Patterns that Require Eventual Positivity or Require Eventual Nonnegativity.
Electronic Journal of Linear Algebra, 19:98-107, 2009/2010.D.D. Olesky, M.J. Tsatsomeros, and P. van den Driessche.
Mv - Matrices : A Generalization of M-matrices Based on Eventually Nonnegative Matrices.
Electronic Journal of Linear Algebra, 18:339-351, 2009.D. Noutsos and M. Tsatsomeros.
On the Numerical Characterization of the Reachability Cone for an Essentially Nonnegative Matrix.
Linear Algebra and its Applications, 430(4):1350-1363, 2009.K. Griffin, J. Stuart, and M. Tsatsomeros.
Noncirculant Toeplitz Matrices All of Whose Powers are Toeplitz.
Chzechoslovak Mathematical Journal, 58(4):1185-1193, 2008.D. Noutsos and M.J. Tsatsomeros.
Reachability and Holdability of Nonnegative States.
SIAM Journal on Matrix Analysis and Applications, 30(2):700-712, 2008.O. Slyusareva and M. Tsatsomeros.
Mapping and Preserver Properties of the Principal Pivot Transform.
Linear and Multilinear Algebra, 56(3):279-292, 2008.K. Griffin and M. Tsatsomeros.
Principal Minors, Part I: A Method for Computing All the Principal Minors of a Matrix.
Linear Algebra and its Applications, 419:107-124, 2006.K. Griffin and M. Tsatsomeros.
Principal Minors, Part II: The Principal Minor Assignment Problem.
Linear Algebra and its Applications, 419:125-171, 2006.
The software associated with the above two papers can be found here.M. Adam and M.J Tsatsomeros.
An Eigenvalue Inequality and Spectrum Localization fo Complex Matrices.
Electronic Journal of Linear Algebra, 15:239-250, 2006.P. Psarrakos and M. Tsatsomeros.
Bounds for Levinger's Function of Nonnegative Almost Skew-symmetric Matrices.
Linear Algebra and its Applications, 416:759-772, 2006.R.Edwards, J.J. McDonald, and M.J. Tsatsomeros.
On Matrices with Common Invariant Cones with Applications to Neural and Gene Networks.
Linear Algebra and its Applications, 398:37-67, 2005.V. Monov and M. Tsatsomeros.
On Reducing and Deflating Subspaces of Matrices.
Electronic Journal of Linear Algebra, 11 : 246-257, 2004.P.J. Psarrakos and M.J. Tsatsomeros.
A Primer of Perron-Frobenius Theory for Matrix Polynomials.
Linear Algebra and its Applications, 393:333-352, 2004.V. Monov and M. Tsatsomeros.
A Criterion for Reducibility of Matrices.
Cybernetics and Information Technologies, 4(2):60--68, 2004.J.J. McDonald, P.J. Psarrakos and M.J. Tsatsomeros.
Almost Skew-Symmetric Matrices.
Rocky Mountain Journal of Mathematics, 34:269-288, 2004.M. Tsatsomeros.
Generating and Detecting Matrices with Positive Principal Minors.
In Focus on Computational Neurobiology, Lei Li, Editor, pp. 115-132, Nova Science, New York, 2004.P.J. Psarrakos and M.J. Tsatsomeros.
The Perron Eigenspace of Nonnegative Almost Skew-Symmetric Matrices and Levinger's Transformation.
Linear Algebra and its Applications, 360:43-57, 2003.J.J. McDonald, D.D. Olesky, M.J. Tsatsomeros, and P. van den Driessche.
On the Spectra of Striped Sign Patterns.
Linear and Multilinear Algebra, 51:39-48, 2003.P.J. Psarrakos and M.J. Tsatsomeros.
Numerical Range: (in) a Matrix Nutshell, Parts 1 / 2.
Mathematical Notes from Washington State University, Vol 45, No. 2, 2002 / Vol 46, No. 1, 2003.S.M. Fallat and M.J Tsatsomeros.
On the Cayley Transform of Positivity Classes of Matrices.
Electronic Journal of Linear Algebra, 9:190-196, 2002.P.J. Psarrakos and M.J. Tsatsomeros.
On the Stability Radius of Matrix Polynomials.
Linear and Multilinear Algebra, 50 : 151-165, 2002.J. Maroulas, P.J. Psarrakos, and M.J. Tsatsomeros.
Perron-Frobenius Type Results on the Numerical Range.
Linear Algebra and its Applications, 348 : 49-62, 2002.S. Kirkland, P.J. Psarrakos, and M.J. Tsatsomeros.
On the Location of the Spectrum of Hypertournament Matrices.
Linear Algebra and its Applications, 323 : 37-49, 2001.M. Tsatsomeros.
A Criterion for the Existence of Common Invariant Subspaces of Matrices.
Linear Algebra and its Applications, 322 : 51-59, 2001.T. Myers and M. Tsatsomeros.
Potash Crystallization.
Report in the Proceedings of the 1st Prairie Industrial Problem Solving Workshop,
August 7-11, 2000, Brandon, Manitoba.J. Maroulas, P.J. Psarrakos, and M.J. Tsatsomeros.
Separable Characteristic Polynomials of Pencils and Property L.
Electronic Journal of Linear Algebra, 7 : 182-190, 2000.G.Y. Lee, J.J. McDonald, B.L. Shader, and M.J. Tsatsomeros.
Extremal Properties of Ray-nonsingular Matrices.
Discrete Mathematics, 216 : 221-233, 2000.M. Tsatsomeros.
Principal Pivot Transforms: Properties and Applications.
Linear Algebra and its Applications, 307 : 151-165, 2000.M. Tsatsomeros and L. Li.
A Recursive Test for P-Matrices.
BIT Numerical Mathematics, 40(2) : 410-414, 2000.P. J. Psarrakos and M. J. Tsatsomeros.
On the Relation Between the Numerical Range and the Joint Numerical Range of Matrix Polynomials.
Electronic Journal of Linear Algebra, 6 : 20-30, 2000.L. Han, M. Neumann, and M. Tsatsomeros.
Spectral Radii of Fixed Frobenius Norm Perturbations of Nonnegative Matrices.
SIAM Journal on Matrix Analysis and Applications, 21 : 79-92, 1999.J.J. McDonald, R. Nabben, M. Neumann, H. Schneider, and M. Tsatsomeros.
Inverse Tridiagonal Z-Matrices.
Linear and Multilinear Algebra, 45 : 75-97, 1998.J.J. McDonald, D.D. Olesky, H. Schneider, M.J. Tsatsomeros, and P. van den Driessche.
Z-Pencils.
Electronic Journal of Linear Algebra, 4 : 32-38, 1998.M. Tsatsomeros.
Sign Controllability: Sign Patterns That Require Complete Controllability.
SIAM Journal on Matrix Analysis and Applications, 19 : 355-364, 1998.B. Li, L. Li, M. Harada, H. Niki, and M. Tsatsomeros.
An Iterative Criterion for H-matrices.
Linear Algebra and Its Applications, 271 : 179-190, 1998.J.J. McDonald, D.D. Olesky, M. Tsatsomeros, and P. van den Driessche.
Ray Patterns of Matrices and Nonsingularity.
Linear Algebra and its Applications, 267 : 359-373, 1997.B. Li and M. Tsatsomeros.
Doubly Diagonally Dominant Matrices.
Linear Algebra and its Applications, 261 : 221-235, 1997.S. Kirkland, J.J. McDonald, and M. Tsatsomeros.
Sign Patterns that Require Positive Eigenvalues.
Linear and Multilinear Algebra, 41 : 199-210, 1996.J.J. McDonald, M. Neumann, H. Schneider, and M. Tsatsomeros.
Inverses of Unipathic M-Matrices.
SIAM Journal on Matrix Analysis and Applications, 17 : 1025-1036, 1996.C.R. Johnson, M. Neumann, and M. Tsatsomeros.
Conditions for the Positivity of Determinants.
Linear and Multilinear Algebra, 40 : 241-248, 1996.C.R. Johnson and M. Tsatsomeros.
Convex Sets of Nonsingular and P-Matrices.
Linear and Multilinear Algebra, 38 : 233-239, 1995.J.J. McDonald, M. Neumann, H. Schneider, and M. Tsatsomeros.
Inverse M-Matrix Inequalities and Generalized Ultrametric Matrices.
Linear Algebra and its Applications, 220 : 321-341, 1995.C.R. Johnson, D.D. Olesky, M. Tsatsomeros, and P. van den Driessche.
An Identity for the Determinant.
Linear and Multilinear Algebra, 36 : 189-194, 1994.D.D. Olesky, M. Tsatsomeros, and P. van den Driessche.
Qualitative Controllability and Uncontrollability by a Single Entry.
Linear Algebra and its Applications, 187 : 183-194, 1993.M. Tsatsomeros, J.S. Maybee, D.D. Olesky, and P. van den Driessche.
Nullspaces of Matrices and Their Compounds.
Linear and Multilinear Algebra, 34 : 291-300, 1993.C.R. Johnson, D.D. Olesky, M. Tsatsomeros, and P. van den Driessche.
Spectra with Positive Elementary Symmetric Functions.
Linear Algebra and its Applications, 180 : 247-262, 1993.J.S. Maybee, D.D. Olesky, M. Tsatsomeros, and P. van den Driessche.
Combinatorial Eigenvalues of Matrices.
Linear Algebra and its Applications, 175 : 213-224, 1992.M. Neumann and M. Tsatsomeros.
Symbiosis Points for Linear Differential Systems.
Linear and Multilinear Algebra, 30 : 49-59, 1991. [References]M. Neumann, R.J. Stern, and M. Tsatsomeros.
The Reachability Cones of Essentially Nonnegative Matrices.
Linear and Multilinear Algebra, 28 : 213-224, 1991. [References]R.J. Stern and M. Tsatsomeros.
Extended M-Matrices and Subtangentiality.
Linear Algebra and its Applications, 97 : 1-11, 1987.
Selected Presentations
Selected Presentations
Envelope: Localizaton of the Spectrum of a Matrix Envelope: Localization of the Spectrum of a Matrix (NASCA, Kalamata 2018)
Lecture notes on P-matrices (GIAN Course, Indian Institute of Technology - Madras, 2017)
Perron-Frobenius Theory and Positivity in Linear Algebra (in honour of Hans Schneider) (ALA, Novi Sad 2010)
Spectrum localization for almost skew-symmetric matrices (BIRS, Banff 2003)
Generating and detecting matrices with positive principal minors (ILAS, Auburn 2002)
Since Ancient Greece (A power point presentation on two "modern" era Greek mathematicians)
Current Editorship
Current Editorship
Advisory Editor (past Co-Editor-In-Chief) of Electronic Journal of Linear Algebra
Associate Editor of Linear Algebra and its Applications
Special Editor
Special Editor
Linear Algebra and its Applications, Vol 341, Issues 1-3, pp. 1-420, 2002
Dedicated to Tsuyoshi Ando in recognition of his 70th birthday.Linear Algebra and its Applications, Vol. 393, pp. 1-432, 2004.
Dedicated to Positivity in Linear Algebra.Linear Algebra and its Applications. Vol. 409, pp. 1-187, 2005.
Dedicated to Pauline van den Driessche.Electronic Journal of Linear Algebra , Vol. 19, pp. 1-140, 2009/2010.
On the occasion of the AIM workshop Nonnegative Matrix Theory: Generalizations and Applications.Linear Algebra and its Applications. Vol. 436, 2012.
Dedicated to the Applied Linear Algebra Conference held in Novi Sad in 2010.
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