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Dr. Zhongshan Li
Professor of Mathematics

Graduate Director of Mathematics

 

Department of Mathematics and Statistics
Georgia State University
Atlanta, GA 30302-4110
Phone: (404) 413-6437
Fax: (404) 413-6403
E-mail: zli@gsu.edu

 


Personal Information

I grew up in Lanzhou, China. In 1983, I obtained my B.Sc. in mathematics from Lanzhou University. Then I spent three years at Beijing Normal University, graduating with a M.Sc. in Mathematics in 1986. After teaching briefly at Hebei Normal College, I went to North Carolina State University, where I got my Ph.D. in mathematics in 1990. For further personal information, you may read my mini autobiography

Research Interests

Combinatorial Matrix Theory
Algebraic Graph Theory

Publications

1.      L. Zhang, T.Z. Huang, Z. Li and J.Y. Zhang, Several spectrally arbitrary ray patterns, Linear and Multilinear Algebra 61(2013), 543-564. 

2.      Z. Li, Y. Gao, M. Arav, F. Gong, W. Gao, F.J. Hall and H. van der Holst, Sign patterns with minimum rank 2 and upper bounds on minimum ranks, Linear and Multilinear Algebra.  In press.

3.      M. Arav, F, Hall, Z. Li and H. van der Holst, The inertia set of a signed graph. LAA. In press

4.      X. Feng, T.Z. Huang, Z. Li, J. Luo and Y. Gao, Sign patterns that allow diagonalizability revisited, Linear and Multilinear Algebra.  In press.

5.      F. Hall and Z. Li, Sign pattern matrices, invited updated chapter (Chapter 33) in the Handbook of Linear Algebra, 2nd edition, CRC Press.  In press.

6.      Y. Shao, Y. Gao and Z. Li, The m-competition indices of symmetric primitive digraphs without loop, Electronic Journal of Linear Algebra 23 (2012), 457-472.

7.      X. Feng, Z. Li and T.Z. Huang, Is every nonsingular matrix diagonally equivalent to a matrix with all distinct eigenvalues? Linear Algebra and Its Applications 436 (2012) , 120-125.

8.      L. Zhang, T.Z. Huang, and Z. Li, Primitive zero-symmetric sign pattern matrices with zero diagonal attaining the maximum base, Journal of Applied Math 2012 (2012), Article ID 276386, 28 pages, doi 10.1155/2012/276386.

9.      M. Arav, Frank Hall, Zhongshan Li, Krishna Kaphle and Nilay Manzagol, Spectrally arbitrary tree sign patterns of order 4, Electronic Journal of Linear Algebra 20 (2010), 180-197.

10.  M. Arav, F. Hall, Z. Li, A. Merid and Y.Gao, Sign patterns that require almost unique rank, Linear Algebra and Its Applications 430 (2009), 7-16.

11.  M. Arav, F. Hall, Z. Li and B. Rao, ZPC matrices and zero cycles, International Journal of Combinatorics 2009 (2009), 1-5.

12.  M. Arav, F. Hall, Z. Li and B. Rao, Rational solutions of certain matrix equations, Linear Algebra and Its Applications 430 (2009), 660-663.

13.  M. Arav, F. Hall and Z. Li, A Cauchy-Schwarz inequality for triples of vectors, Mathematical Inequalities and Applications 11 (2008), 629-634.

14.  Y. Gao, Z. Li and Y. Shao, A note on spectrally arbitrary sign patterns, JP Journal of Algebra, Number Theory and Applications 11 (2008), 15-35

15.  T. Huang, G. Mou, G. Tian, Z. Li, D. Wang, Subdirect sums of P (P0)-matrices and totally nonnegative matrices, Linear Algebra and Its Applications 429 (2008), 1730-1743.

16.  Y. Gao, Z. Li and Y Shao, Sign patterns allowing nilpotence of index 3, Linear Algebra and Its Applications 424 (2007), 55-70.

17.  F. Hall and Z. Li, Sign pattern matrices, invited chapter in the Handbook of Linear Algebra, CRC Press, 2007.

18.  Marina Arav, F. Hall, S. Koyuncu, Z. Li and  B. Rao,  Rational realizations of the minimum rank of a sign pattern matrix, Linear Algebra and Its Applications  411 (2005), 111-125. 

19.  Z. Li, F. Hall and J. Stuart, Reducible powerful ray pattern matrices, Linear Algebra and Its Applications 399 (2005), 125-140.

20.  F. Hall, Z. Li and B. Rao, From Boolean to Sign Pattern Matrices, Linear Algebra and Its Applications 393 (2004), 233-251.

21.  G. Chen, G. Davis, F. Hall, Z. Li, K. Patel, M. Stewart, An interlacing result on normalized Laplacians,  SIAM Journal on Discrete Mathematics 18 (2004), 353-361.

22.  G. Chen, F. Hall, Z. Li and B. Wei, On Ranks of Matrices Associated with Trees, Graphs and Combinatorics 19 (2003), 323-334.

23.  F. Hall and Z. Li, Sign Patterns, Inverses and Generalized Inverses - A Brief Survey, Numerical Mathematics: A Journal of Chinese Universities 12 (Supplement) (2003), 8-11.

24.  G. Chen, F. Hall, Z. Li and B. Wei, On Ranks of Matrices Associated with Trees, Numerical Mathematics: A Journal of Chinese Universities 12 (Supplement) (2003), 76 - 79.

25.  Z. Li, F. Hall and J. Stuart, Irreducible Powerful Ray Pattern Matrices, Linear Algebra and Its Applications 342(2002), 47-58. 

26.  Z. Li and L. Harris, Sign Patterns That Require All Distinct Eigenvalues, JP Journal of Algebra, Number Theory and Applications 2 (2) (2002), 161-179.

27.  G. Chen, F. Hall, A. Kezdy, Z. Li and H. Zhou, Isomorphisms Involving Reversing Arcs of Digraphs, Journal of Combinatorial Theory and Combinatorial Computing 36 (2001), 155-160.

28.  F. Hall, Z. Li and D. Wang, Symmetric Sign Pattern Matrices That Require Unique Inertia, Linear Algebra and Its Applications 338(2001), 153-169.

29.  F. Hall and Z. Li, Inertia Sets of Certain Symmetric Sign Pattern Matrices, Numerical Mathematics: A Journal of Chinese Universities 10(2001), 226-240.

30.  C. Eschenbach, F. Hall and Z. Li, Eigenvalue Distribution of Certain Ray Patterns, Czechoslovak Mathematical Journal 50(125) (2000), 749-762.

31.  C. Eschenbach, F. Hall, R. Hemasinha, S. Kirkland, Z. Li, B. Shader, J. Stuart and J. Weaver, On a Special Class of Almost Regular Tournament Matrices, Linear Algebra and Its Applications 306 (2000), 103-121.

32.  C. Eschenbach, F. Hall, R. Hemasinha, S. Kirkland, Z. Li, B. Shader, J. Stuart and J. Weaver, Properties of Tournaments among Well Matched Players, the American Mathematical Monthly 107(2000), No. 10, 881-892.

33.  C. Eschenbach, F. Hall, D. Harrell and Z. Li, When Does the Inverse Have the Same Sign Pattern as the Transpose?, Czechoslovak Mathematical Journal 49(124) (1999), no. 2, 255--275.

34.  F. Hall and Z. Li, Sign Patterns of Idempotent Matrices, Korean Journal of Mathematics 36 (1999), No. 3, 469-487.

35.  C. Eschenbach and Z. Li, Potentially Nilpotent Sign Pattern Matrices, Linear Algebra and Its Applications, 299 (1999), 81-99.

36.  C. Eschenbach, F. Hall and Z. Li, From Real to Complex Sign Patterns, Bulletin of the Australian Mathematical Society 57(1998), 159-172.

37.  C. Eschenbach and Z. Li, How Many Negative Entries Can A^2 Have?, Linear Algebra and Its Applications 254 (1997), 99-117.

38.  Z. Li, F. Hall and F. Zhang, Sign Patterns of Nonnegative Normal Matrices, Linear Algebra and Its Applications 254 (1997), 335-354.

39.  C. Eschenbach, F. Hall, C. Johnson and Z. Li, The Graphs of Unambiguous Entries in the Product of Two (+,-) Sign Patterns, Linear Algebra and Its Applications 260 (1997), 95-118.

40.  C. Eschenbach, F. Hall and Z. Li, Some Sign Patterns That Allow an Inverse Pair B and B^{-1} , Linear Algebra and Its Applications 252(1997), 299-321.

41.  Z. Li, F. Hall and C. Eschenbach, The Structure of Nonnegative Cyclic Matrices, Linear and Multilinear Algebra 41 (1996), 23-33.

42.  C. Eschenbach, F. Hall and Z. Li, Eigenvalue Frequency and Consistent Sign pattern Matrices, Czechoslovak Mathematical Journal 44(1994), 461-479.

43.  Z. Li, F. Hall and C. Eschenbach, On the Period and Base of a Sign Pattern Matrix, Linear Algebra and Its Applications 212 (1994), 101-120.

44.  C. Eschenbach, F. Hall and Z. Li, Sign Pattern Matrices and Generalized Inverses, Linear Algebra and Its Applications 211(1994), 53-66.

45.   Z. Li, A Determinantal Description of GCD-closed Sets and k-sets, Linear and Multilinear Algebra 31(1992), 245-250.

46.  Z. Li, The Determinants of GCD Matrices, Linear Algebra and Its Applications 134(1990), 137-143.

47.  Z. Li, The Embedding of Rings in Regular Rings and \pi-regular rings, Ph.D. dissertation, North Carolina State University, 1990.

48.  Z. Li, On Principal Torsion Theory Rings, M.SC. thesis, Beijing Normal University, 1986.

49.  Z. Li, On Unique Factorization of Languages over a Free Monoid, B. Sc. Thesis, Lanzhou University, 1983.

Editorial Activity

I am a member of the Editorial Boards of Algebra and JP Journal of Algebra, Number Theory and Applications.

Please refer to my curriculum vitae for further information concerning my professional activities.

Algebra and Discrete Mathematics Seminar

Schedule for Fall 2010: Friday afternoons at 12:45 pm, Erdos Conference Room (COE 796)

Date                Speaker                                   Topic

9/18                 Dr. Yongwei Yao                   Primary decompositions

9/25                 Dr. Christian Avart                 Colorful flowers

10/2                 Dr. Zhongshan Li                    Sign patterns that require all distinct eigenvalues

10/16               Dr. Yi Zhao                             Finding trees in dense graphs

            10/23               Dr. Florian Enescu                  Multiplicity in algebra and geometry (Part 1)

11/6                 Dr. Florian Enescu                  Multiplicity in algebra and geometry (Part 2)

11/13               Dr. Frank Hall             Some interlacing inequalities

11/20               Dr. Guantao Chen                   Graph edge coloring involving edge density

2/26                 Dr. Florian Enescu                  The motivation behind schemes

3/5                   Dr. Hua Wang             Two subtree problems

3/26                 Dr. Zhongshan Li                    The field of values of matrix

4/16                 Dr. Yongwei Yao                   Zero divisor graphs of commutative rings

 

Courses Recently Taught

 

Math 1070 Elementary Statistics

Math 1113 Precalculus
Math 1220 Survey of Calculus
Math 2211 Calculus of One Variable I
Math 2212 Calculus of One Variable II
Math 2215 Multivariate Calculus

Math 2420 Discrete Mathematics
Math 3000 Bridge to Higher Mathematics
Math 3435 Introductory Linear Algebra

Math 4435/6435 Linear Algebra

Math 4441/6441 Abstract Algebra

Math 4450/6450 Theory of Numbers

Math 4661/6661 Analysis I

Math 4662/6662 Analysis II
Math 8200 Advanced Matrix Analysis

Math 8210 Topics in Applied Matrix Analysis
Math 8220 Abstract Algebra I


Photo Gallery

Angela and Andrew with Grandpa in Dunhuang, 2008

Ying and Zhongshan at Qinghai Lake, 2009

Ying and Zhongshan in Chengdu, 2008

Ying and Zhongshan in Hangzhou, 2008

Ying and Zhongshan in Shanghai, 2008

Angela and Andrew in 1997

Andrew at Kindergarten

Angela as a 2nd grader in 2000

Trick or Treat?

Andrew in Tuxedo