Fuzhen Zhang, Ph.D.

Professor
Department of Mathematics
(954) 262-8317
zhang@nova.edu

Education:

Research Interest(s):

Courses Taught:

My research work is in the areas of matrix analysis, linear and multilinear algebra, operator theory, and combinatorics.
  1. Polytopes of Stochastic Tensors, with H. Chang and V. Paksoy, Accepted for publication in Annals of Functional Analysis, 2015.
  2. Interpretation of Generalized Matrix Functions via the Geometric Measure of Entanglement, with H. Chang and V. Paksoy, accepted for publication in International Journal of Quantum Information, DOI: 10.1142/S0219749915500495, 2015
  3. Positivity of partitioned Hermitian matrices with unitarily invariant norms, with C.-K. Li, Positivity, Volume 19, Issue 3, pp 439-444, September 2015.
  4. An inequality for tensor product of positive operators and its applications, with Haixia Chang and Vehbi E. Paksoy, Linear Algebra Appl., doi:10.1016/j.laa.2014.12.026
  5. A matrix decomposition and its applications, Linear and Multilinear Algebra, Volume 63, Issue 10, October 2015, pages 2033-2042.
  6. Angles, triangle inequalities, correlation matrices and metric-preserving and subadditive func-tions, with D. Castano and V.E. Paksoy, Linear Algebra Appl., doi:10.1016/j.laa.2014.10.011
  7. Book Review: Topics in Quaternion Linear Algebra (Princeton University Press, 2014) by Leiba Rodman, International Linear Algebra Society (ILAS) Bulletin IMAGE, No.54, pp.25– 26, Spring 2015.
  8. Book Review for Matrix Theory (American Mathematical Society, 2013) by Xingzhi Zhan, x+253 pp, Hardback, ISBN 978-0-8218-9491-0, Linear Algebra Appl. 471(2015) 1–9.
  9. Inequalities of generalized matrix functions via tensor products, with Vehbi E. Paksoy and Ramazan Turkmen, Electron. J. Linear Algebra, Vol. 27, pp. 332–341, 2014.
  10. Schur Complements, book chapter, with R. Horn, in Handbook of Linear Algebra , Second Edition (Discrete Mathematics and Its Applications) by L. Hogben, CRC Press, 2014.
  11. Integral Majorization Polytopes, with GEIR DAHL, Discrete Mathematics, Algorithms and Applications, Vol. 5, No. 3 (2013) 1350019 (12 pages)
  12. Chaos analysis and control for a class of SIR epidemic model with seasonal fluctuation, with Yi Zhang, Q.-L. Zhang, and F. Bai, Int’l J. Biomathematics, Vol.6, No.1 (2013) (11 pages).
  13. An analytic approach to a permanent conjecture, Linear Algebra Appl. 438 (2013) 1570–1579.
  14. A generalization of the complex Autonne-Takagi factorization to quaternion matrices, with R. Horn, Linear & Multilinear Algebra, 60 (2012) 11-12, 1239–1244.
  15. Some inequalities of majorization type, with R. Turkmen and V. Palsoy, Linear Algebra Appl. 437 (2012) 1305–1316.
  16. Book Review for Inequalities: Theory of Majorization and Its Applications (Springer Series in Statistics) by A.W. Marshall, I. Olkin and B.C. Arnold, 2nd edition, Springer (2011), xxvii+909 pp, Hardback, ISBN 978-0-387-40087-7, Linear Algebra Appl. 436(2012)1535–1540.
  17. Positivity of matrices with generalized matrix functions, Acta Mathematica Sinica, English Series, Volume 28, Number 9 (2012) 1779–1786.
  18. On the Unitary Diagonalisation of a Special Class of Quaternion Matrices, with Clive Cheong Took and Danilo P. Mandic, Applied Math Lett. 24 (2011) 1806–1809.
  19. On the eigenvalues of quaternion matrices, with F. O. Farid and Q.-W. Wang, Linear & Multilinear Algebra, Vol. 59, No. 4, 2011, pp. 451–473.
  20. Contractive matrices of Hua type, with C. Xu and G. Xu, Linear & Multilinear Algebra, Vol. 59, No. 2, 2011, pp. 159–172.
  21. Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefininte matrices, with R. Horn, Electron. J. Linear Algebra, Vol. 20, pp. 90–94, 2010.
  22. Robustness analysis of descriptor systems with parameter uncertainties, with C. Yang, Q. Zhang, and Z. Zhou, International Journal of Control, Automation, and Systems 8(2) (Apr. 2010): 204–209.
  23. Criteria and Schur Complements of H-matrices, with J. Liu, J. of Mathematics Applications and Computation, Spring (2010) 32:119–133.
  24. New Results and Problems on Hua Matrices, with C. Xu and G. Xu, Proceedings of 3rd International Workshop on Matrix Analysis, pp.228–232, July 9-13, 2009.
  25. Revisiting Hua-Marcus-Bellman-Ando Inequalities on Contractive Matrices, with C. Xu and Z. Xu, Linear Algebra Appl. 430 (2009) 1499–1508.
  26. An operator equality involving a continuous field of operators and its norm inequalities, with M. Sal Moslehian, Linear Algebra Appl. 429 (2008) 2159–2167.
  27. Hua’s matrix equality and Schur complements, with C. Paige, G. Styan, and B. Wang, Inter-national Journal of Information & Systems Sciences, Vol.4, No.1, pp.124–135, March 2008.
  28. On the Operator Bohr Inequality, J. of Math. Anal. and Appl. 333 (2007) 1264–1271.
  29. Gersgorin type theorems for quaternionic matrices, Linear Algebra Appl. 424 (2007) 139–153.
  30. Relative perturbation bounds for the eigenvalues of diagonalizable and singular matrices – Application of perturbation theory for simple invariant subspaces, with Y. Wei, X. Li, and F. Bu, Linear Algebra Appl. 419 (2006) 765–771.
  31. Eigenvalue inequalities for matrix product, with Q. Zhang, IEEE Trans. Auto. Contr., Vol. 51, No. 9, pp. 1506–1509, Sept., 2006.
  32. Book chapter: Chapter 1 Basic Properties of the Schur Complement, with R. Horn, The Schur Complement and Its Applications, pp. 17–46, Springer, New York, 2005.
  33. Book chapter: Chapter 3 Block Matrix Techniques, The Schur Complement and Its Applica-tions, pp. 83–110, Springer, New York, 2005.
  34. Disc separation of the Schur complement of diagonally dominant matrices and determinantal bounds, with J. Liu, SIAM J. Matrix Anal. Appl., Vol. 27, No. 3, pp. 665–674, Dec. 2005.
  35. Matrix Inequalities by Means of Embedding, with T-G Lei and C-W Woo, Electron. J. Linear Algebra, Vol. 11, pp. 66–67, 2004.
  36. Matrix Identity on the Schur Complement, Linear & Multilinear Algebra, Vol 52, No. 5, pp. 367–373, 2004.
  37. The Schur Complements of Generalized Doubly Diagonally Dominant Matrices, with J. Liu and Y. Huang, Linear Algebra Appl. 378 (2004) 231–244.
  38. On the Schur Complement of Diagonally Dominant Matrices, with Lei, Woo, Liu, SIAM Proceedings on Applied Linear Algebra Conference, Williamsburg, CP13, July 2003.
  39. Block Matrix Techniques and Matrix Inequalities, Numerical Mathematics, with S. Tang, Vol.
  40. Supplement, pp. 15–20, May 2003, Proceedings of the 5th China Matrix Theory and Its Applications - International Congress of Mathematicians (ICM) Satellite Conference, May 2002.
  41. Matrix Inequalities by Means of Block Matrices, Mathematical Inequalities and Applications, Vol. 4, Number 4, pp. 481–490, October 2001.
  42. Jordan Canonical Form of a Partitioned Complex Matrix and Its Applications to Real Quater-nion Matrices, with Y. Wei, Communications in Algebra, 29(6) 2363–2375 (2001)
  43. Equivalence of the Wielandt inequality and the Kantorovich inequality, Linear and Multilinear Algebra, Vol. 48, pp. 275–279, 2001.
  44. Schur Complements and Matrix Inequalities in L¨owner Ordering, Linear Algebra Appl. 321 (2000) 399–410.
  45. Equivalence of a matrix product to the Kronecker product, with Y. Wei, Hadronic J. Supple-ment, 15, pp. 327–332, 2000.
  46. On the Hadamard Product of Inverse M-matrices, with B-Y Wang and X. Zhang, Linear Algebra Appl. 305 (2000) 23–31.
  47. Some Inequalities on Generalized Schur Complements, with B-Y Wang and X. Zhang, Linear Algebra Appl. 302-303 (1999) 163–172.
  48. Some Inequalities for Sum and Product of positive Semidefinite Matrices, with B-Y Wang and B-Y Xi, Linear Algebra Appl. 293 (1999) 39–49.
  49. An analogue of Hua’s Determinantal Inequality, with B-Y Wang, Hunan Annals of Mathemat-ics (China), Vol. 18, No. 3, pp. 5–6, 1998.
  50. On the Precise Number of (0,1)-Matrices in A(R,S), with B-Y Wang, Discrete Mathematics, Vol. 187, pp. 211–220, 1998.
  51. On Normal Matrices of Zeros and Ones with Fixed Row Sum, with B-Y Wang, Linear Algebra Appl. 275/276 (1998) 617–626.
  52. 51. On 0-1 Symmetric and Normal Matrices, with B-Y Wang, J. of Math Research and Exposition (China), Vol. 18, No. 2, pp. 159–164, May, 1998.
  53. Schur Complements and Matrix Inequalities of Hadamard Products, with B-Y Wang, Linear and Multilinear Algebra, Vol. 43, pp. 315–326, 1997.
  54. Norm Hull of Vectors and Matrices, with C-K Li and N-K Tsing, Linear Algebra Appl. 257 (1997) 1–27.
  55. Sign Patterns of Nonnegative Normal Matrices, with Z. Li and F. Hall, Linear Algebra Appl. 254 (1997) 335–354.
  56. Quaternions and Matrices of Quaternions, Linear Algebra Appl. 251 (1997) 21–57.
  57. The Generalized Numerical Range with Completely Symmetric Function, with T-G Lei, Acta Mathematica Sinica, Vol. 39, No. 5, pp. 590–596, 1996.
  58. Words and Normality of Matrices, with B-Y Wang, Linear and Multilinear Algebra, Vol. 40, No. 2:111–118, 1995.
  59. An Operator Inequality and Matrix Normality, with Charles R Johnson, Linear Algebra Appl.
  60. 240 (1995) No. 1–3, pp. 105–110.
  61. Trace and Eigenvalue Inequalities of Ordinary and Hadamard Products for Positive Semidef-inite Hermitian Matrices, with B-Y Wang, SIAM Matrix Analysis and Applications, Vol. 16, No. 4, pp. 1173–1183, 1995.
  62. On Numerical Range of Normal Matrices of Quaternions, Journal of Mathematical and Physical Sciences, Vol. 29, No. 6, pp.235–251, 1995.
  63. Erratum “Robison-Taussky inequality”, with C. R. Johnson, Linear and Multilinear Algebra, Vol. 38, No. 3, p. 281, 1995.
  64. A Trace Inequality for Unitary Matrices, with B-Y Wang, The American Mathematical Monthly, Vol. 101, Number 5, pp. 453–455, 1994.
  65. The Numerical Range of Normal Matrices with Quaternion Entries, with W. So and R. C. Thompson, Linear and Multilinear Algebra, Vol. 37, pp. 175–195, 1994.
  66. Two Conjectures on Permanents, with G. Liang and W. So, Linear Algebra Appl. 197&198 (1994) 840–844.
  67. A Majorization Conjecture for Hadamard Products and Compound Matrices, Linear and Mul-tilinear Algebra, Vol. 33, No. 4, p. 301–303, 1993.
  68. Some Inequalities for the Eigenvalues of the Product of Positive Semi-definite Hermitian Matrices, with Bo-Ying Wang, Linear Algebra Appl. 160 (1992) 113–118.
  69. Notes on Hadamard Products of Matrices, Linear and Multilinear Algebra, Vol. 25, pp. 237– 242, 1989.
  70. Some Identities of Permanents, Mathematics in Practice and Theory (in Chinese), No. 1, pp. 44–47, 1989.
  71. Another Proof of a Singular Value Inequality Concerning Hadamard Products of Matrices, Linear and Multilinear Algebra, Vol. 22, pp. 307–311, 1988.
  72. Solution to a Conjecture of Marcus, Kidman, and Sandy, J. of Beijing Normal University (Nature Sci.), Supplement No. 2, pp. 14–18, 1988.
  73. On Eigenvalue and Singular Value Inequalities for Matrix Product, with B.-Y. Wang, J. of Beijing Normal University (Nature Sci.), No. 3, pp. 1–4, 1987.
  74. On the Best Euclidean Fit to a Distance Matrix, J. of Beijing Normal University (Nature Sci.), No. 4, pp. 21–24, 1987.
  75. Some Notes on “The inequality of Hermitian Square Matrices”, Mathematics in Practice and Theory (in Chinese), No. 2, pp. 60–61, 1987.

1. Polytopes of Stochastic Tensors (plenary invited speaker), Recent Advances in Linear Algebra and Graph Theory, University of Tennessee - Chattanooga, March 5-6, 2016.

2. Determinant, permanent, Tensors and Words, University of Miami, Miami, April 20, 2015.

3. Angles between vectors and beyond, the 19th International Linear Algebra Conference, Seoul, South Korea, August 5-9, 2014.

4.  Integral Majorization (invited speaker), 22nd  International Workshop on Matrices and Statistics, Fields Institute, University of Toronto, Canada (http://www.fields.utoronto.ca/programs/scientific/13-14/IWMS), Aug. 12-15, 2013.

5. Generalized Matrix Functions (invited plenary speaker),  18th International Linear Algebra Society Conference, Providence, RI (http://www.ilas2013.com), June 3-7, 2013.