Fuzhen Zhang s Publication List

Fuzhen Zhang s Publication List Papers in peer-reviewed journals 1. 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. 2. 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. 3. INTEGRAL MAJORIZATION POLYTOPES, with GEIR DAHL, Discrete Mathematics, Algorithms and Applications, Vol. 5, No. 3 (2013) 1350019 (12 pages) 4. 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). 5. An analytic approach to a permanent conjecture, Linear Algebra Appl. 438 (2013) 1570 1579. 6. A generalization of the complex Autonne-Takagi factorization to quaternion matrices, with R. Horn, Linear & Multilinear Algebra, 60 (2012) 11-12, 1239 1244. 7. Some inequalities of majorization type, with R. Turkmen and V. Palsoy, Linear Algebra Appl. 437 (2012) 1305 1316. 8. 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. 9. Positivity of matrices with generalized matrix functions, Acta Mathematica Sinica, Volume 28, Number 9 (2012) 1779 1786. 10. 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. 11. 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. 12. Contractive matrices of Hua type, with C. Xu and G. Xu, Linear & Multilinear Algebra, Vol. 59, No. 2, 2011, pp. 159 172. 13. 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. 14. 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. 15. Criteria and Schur Complements of H-matrices, with J. Liu, J. of Mathematics Applications and Computation, Spring (2010) 32:119 133. 16. 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. 17. Revisiting Hua-Marcus-Bellman-Ando Inequalities on Contractive Matrices, with C. Xu and Z. Xu, Linear Algebra Appl. 430 (2009) 1499 1508. 18. An operator equality involving a continuous field of operators and its norm inequalities, with M. Sal Moslehian, Linear Algebra Appl. 429 (2008) 2159 2167. 19. Hua s matrix equality and Schur complements, with C. Paige, G. Styan, and B. Wang, International Journal of Information & Systems Sciences, Vol.4, No.1, pp.124 135, March 2008. 1

20. On the Operator Bohr Inequality, J. of Math. Anal. and Appl. 333 (2007) 1264 1271. 21. Gersgorin type theorems for quaternionic matrices, Linear Algebra Appl. 424 (2007) 139 153. 22. 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. 23. Eigenvalue inequalities for matrix product, with Q. Zhang, IEEE Trans. Auto. Contr., Vol. 51, No. 9, pp. 1506 1509, Sept., 2006. 24. 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. 25. Book chapter: Chapter 3 Block Matrix Techniques, The Schur Complement and Its Applications, pp. 83 110, Springer, New York, 2005. 26. 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. 27. Matrix Inequalities by Means of Embedding, with T-G Lei and C-W Woo, Electron. J. Linear Algebra, Vol. 11, pp. 66 67, 2004. 28. Matrix Identity on the Schur Complement, Linear & Multilinear Algebra, Vol 52, No. 5, pp. 367 373, 2004. 29. The Schur Complements of Generalized Doubly Diagonally Dominant Matrices, with J. Liu and Y. Huang, Linear Algebra Appl. 378 (2004) 231 244. 30. On the Schur Complement of Diagonally Dominant Matrices, with Lei, Woo, Liu, SIAM Proceedings on Applied Linear Algebra Conference, Williamsburg, CP13, July 2003. 31. Block Matrix Techniques and Matrix Inequalities, Numerical Mathematics, with S. Tang, Vol. 12, 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. 32. Matrix Inequalities by Means of Block Matrices, Mathematical Inequalities and Applications, Vol. 4, Number 4, pp. 481 490, October 2001. 33. Jordan Canonical Form of a Partitioned Complex Matrix and Its Applications to Real Quaternion Matrices, with Y. Wei, Communications in Algebra, 29(6) 2363 2375 (2001) 34. Equivalence of the Wielandt inequality and the Kantorovich inequality, Linear and Multilinear Algebra, Vol. 48, pp. 275 279, 2001. 35. Schur Complements and Matrix Inequalities in Löwner Ordering, Linear Algebra Appl. 321 (2000) 399 410. 36. Equivalence of a matrix product to the Kronecker product, with Y. Wei, Hadronic J. Supplement, 15, pp. 327 332, 2000. 37. On the Hadamard Product of Inverse M-matrices, with B-Y Wang and X. Zhang, Linear Algebra Appl. 305 (2000) 23 31. 38. Some Inequalities on Generalized Schur Complements, with B-Y Wang and X. Zhang, Linear Algebra Appl. 302-303 (1999) 163 172. 39. 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. 2

40. An analogue of Hua s Determinantal Inequality, with B-Y Wang, Hunan Annals of Mathematics (China), Vol. 18, No. 3, pp. 5 6, 1998. 41. On the Precise Number of (0,1)-Matrices in A(R, S), with B-Y Wang, Discrete Mathematics, Vol. 187, pp. 211 220, 1998. 42. On Normal Matrices of Zeros and Ones with Fixed Row Sum, with B-Y Wang, Linear Algebra Appl. 275/276 (1998) 617 626. 43. 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. 44. Schur Complements and Matrix Inequalities of Hadamard Products, with B-Y Wang, Linear and Multilinear Algebra, Vol. 43, pp. 315 326, 1997. 45. Norm Hull of Vectors and Matrices, with C-K Li and N-K Tsing, Linear Algebra Appl. 257 (1997) 1 27. 46. Sign Patterns of Nonnegative Normal Matrices, with Z. Li and F. Hall, Linear Algebra Appl. 254 (1997) 335 354. 47. Quaternions and Matrices of Quaternions, Linear Algebra Appl. 251 (1997) 21 57. 48. The Generalized Numerical Range with Completely Symmetric Function, with T-G Lei, Acta Mathematica Sinica, Vol. 39, No. 5, pp. 590 596, 1996. 49. Words and Normality of Matrices, with B-Y Wang, Linear and Multilinear Algebra, Vol. 40, No. 2:111 118, 1995. 50. An Operator Inequality and Matrix Normality, with Charles R Johnson, Linear Algebra Appl. 240 (1995) No. 1 3, pp. 105 110. 51. Trace and Eigenvalue Inequalities of Ordinary and Hadamard Products for Positive Semidefinite Hermitian Matrices, with B-Y Wang, SIAM Matrix Analysis and Applications, Vol. 16, No. 4, pp. 1173 1183, 1995. 52. On Numerical Range of Normal Matrices of Quaternions, Journal of Mathematical and Physical Sciences, Vol. 29, No. 6, pp.235 251, 1995. 53. Erratum Robison-Taussky inequality, with C. R. Johnson, Linear and Multilinear Algebra, Vol. 38, No. 3, p. 281, 1995. 54. A Trace Inequality for Unitary Matrices, with B-Y Wang, The American Mathematical Monthly, Vol. 101, Number 5, pp. 453 455, 1994. 55. 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. 56. Two Conjectures on Permanents, with G. Liang and W. So, Linear Algebra Appl. 197&198 (1994) 840 844. 57. A Majorization Conjecture for Hadamard Products and Compound Matrices, Linear and Multilinear Algebra, Vol. 33, No. 4, p. 301 303, 1993. 58. 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. 59. Notes on Hadamard Products of Matrices, Linear and Multilinear Algebra, Vol. 25, pp. 237 242, 1989. 60. Some Identities of Permanents, Mathematics in Practice and Theory (in Chinese), No. 1, pp. 44 47, 1989. 3

61. Another Proof of a Singular Value Inequality Concerning Hadamard Products of Matrices, Linear and Multilinear Algebra, Vol. 22, pp. 307 311, 1988. 62. Solution to a Conjecture of Marcus, Kidman, and Sandy, J. of Beijing Normal University (Nature Sci.), Supplement No. 2, pp. 14 18, 1988. 63. 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. 64. On the Best Euclidean Fit to a Distance Matrix, J. of Beijing Normal University (Nature Sci.), No. 4, pp. 21 24, 1987. 65. Some Notes on The inequality of Hermitian Square Matrices, Mathematics in Practice and Theory (in Chinese), No. 2, pp. 60 61, 1987. Theses 66. Permanent Inequalities and Quaternion Matrices, Ph.D. Dissertation, University of California, Santa Barbara, May 1993. 67. Inequalities Concerning Hadamard Products of Matrices, The thesis for M.S. Degree, April 1987. (Collected in Best Thesis Collection of Beijing Normal University 1997) Books 68. Counterexamples in Matrix Analysis, manuscript, 200+ pages. 69. The Schur Complement and Its Applications, Editor (chapter contributors T. Ando, C. Brezinski, R. Horn, C. Johnson, J.-Z. Liu, S. Puntanan, R. Smith, G. P. H. Styan, and F. Zhang), Springer, New York, 2005. 70. Matrix Theory: Basic Results and Techniques, Springer, New York, 1999. 2nd edition, 2011; 1st edition, 1999. 71. Linear Algebra: Challenging Problems for Students, Johns Hopkins University Press, Baltimore, 1996. 2nd edition, May 2009; 1st edition 1996. 72. Translation from English to Chinese of Marcus and Minc s book: A Survey of Matrix Theory and Matrix Inequalities, with Jipei Du, Dalian University of Technology Press, Dalian, China, 1990. Problems posed or solved, etc. - Excluding referee reports or math reviews 73. Problem 52-5: Matrix Hadamard Power, with Roger Horn, International Linear Algebra Society (ILAS) Bulletin IMAGE, No.52, p.48, Spring 2014. 74. Report on The 4th International Conference on Matrix Analysis and Applications Konya, Turkey, July 2-5, 2013, Report by Ramazan Trkmen and Fuzhen Zhang, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 51, p. 25, Fall 2013. 75. Solution to IMAGE Problem 50-3: Trace Inequality for Positive Block Matrices, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 51, p. 38, Fall 2013. 76. Solution to Problem 49-2: Matrix Diagonal Entries, with R. Horn, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 50, p. 40, Spring 2013. 4

77. Problem 49-2: Matrix Diagonal Entries, with R. Horn, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 49, p. 52, Fall 2012. 78. Problem 47-7: Singular Value Inequalities, with R. Turkmen, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 47, p. 40, Fall 2011. 79. Problem 46-7: Trace Inequality of a Positive Semidefinite Matrix with Exponential Function, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 46, p. 48, Spring 2011. 80. Problem 45-4: Nilpotent 0-1 Matrix, with R. Horn, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 45, p. 48, Fall 2010. 81. Problem 11488 of American Mathematical Monthly, with D. Merino, The American Mathematical Monthly, Vol.117, No. 3, March 2010. 82. Report: Ky Fan (1914 2010) International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 44, p. 15, Spring 2010. 83. Problem 43-7: Three Positive Definite Matrices, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 43, p. 44, Fall 2009. 84. Solution 41-9.2 to the problem proposed by G. Goodson and R. Horn, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 42, p. 34, Spring 2009. 85. Problem 42-6: Positive Semidefinite Matrices, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 42, p. 40, Spring 2009. 86. Problem 41-14: Minimum Eigenvalue of a Special Matrix, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 41, p. 44, Fall 2008. 87. Conference Report: 1st International Workshop on Matrix Analysis and Applications, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 35, p. 24, Fall 2005. 88. Book Review for Generalized Inverses: Theory and Computations by G. Wang and Y. Wei, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 34, p. 13, Spring 2005. 89. Conference Report: Morris Newman California Matrix Conference, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 32, p. 12, April 2004. 90. Conference Report: International Conference on Matrix Analysis and Applications, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 32, p. 13, April 2004. 91. Problem 31-8: Eigenvalues and Eigenvectors of a Particular Tridiagonal Matrix, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 31, p. 43, Oct., 2003. 92. Solution 29-5.5 to the problem proposed by J. Gross and G. Trenkler, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 30, p. 25, April, 2003. 93. Report on the China Matrix Meeting - ICM Satellite Meeting, with E. Jiang, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 29, p. 8, Oct., 2002. 94. Florida Matrix Analysis Conference Announcement, with C-K Li, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 29, p. 12, Oct., 2002. 95. Solution 28-9.1 to the problem proposed by Y. Wei and F. Zhang, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 29, p. 33, Oct., 2002. 96. Solution 27-3.1 to the problem proposed by C. R. Johnson, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 28, p. 31, April, 2002. 97. Problem 28-9: A Relative Perturbation Bound, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 28, p. 35, April, 2002. 5

98. Problem 28-10: Inequalities involving Square Roots, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 28, p. 35, April, 2002. 99. Solution 25-1.4 to the problem proposed by J. Gross and S. Troschke, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 26, p. 4, April, 2001. 100. Solution 25-7.2 to the problem proposed by S. Drury, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 26, p. 12, April, 2001. 101. Problem 25-8: Several Matrix Orderings involving Matrix Geometric and Arithmetic Means, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 25, p. 17, Oct., 2000. 102. Problem 24-6: Rank of a Principal Submatrix, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 24, p. 17, April, 2000. 103. Problem 24-7: Partitioned Positive Semidefinite Matrices, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 24, p. 17, April, 2000. 104. Problem 24-8: An Inequality involving Hadamard Products, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 24, p. 17, April, 2000. 105. Characterization of a Square Matrix in an Inner-product Inequality, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 22, Problem 22-7, p. 32, April, 1999. 106. Solution 21-1.2 to the Problem proposed by L. Elsner, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 22, p. 27, April, 1999. 107. Solution 21-4.1 to the Problem proposed by G. Trenkler, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 22, p. 30, April, 999. 108. Report on Chinese matrix Conference, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 21, p. 16, 1998. 109. Matrix Similarity, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 20, Problem 20 5, p. 32, 1998. 110. Nonnegative Definiteness and Square Roots, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 20, Problem 20-6, p. 32, 1998. 111. Book Review: Nonnegative Matrices and Applications by R. Bapat and T. Raghavan, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 20, p. 2, April, 1998. 112. Solution 22-7.1 to the Problem proposed by F. Zhang, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 23, p. 27, Oct., 1999. 113. On a Characterization Associated with the Matrix Arithmetic and Geometric Means: Solution to 17-2-3, with C-K Li, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 18, p. 31, 1997. 114. Proposed Problem #10513: Positivity of a Block Matrix, The American Mathematical Monthly, p. 267, June, 1996. 115. Solution to a problem in Econometric Theory, Vol. 12, pp. 585-595, with G. P. H. Styan, 1996. 116. Robert Charles Thompson, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 16, pp. 5-6, 1996. 117. A Determinantal Inequality, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 16, Problem 16-1, p. 32, 1996. 6

118. A Hadamard Product Inequality, International Linear Algebra Society (ILAS) Bulletin IM- AGE, No. 16, Problem 16-2, p. 32, 1996. 7