Fuzhen Zhang s Publication and Presentation List (updated Dec. 2007)

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1 Fuzhen Zhang s Publication and Presentation List (updated Dec. 2007) Papers in peer-reviewed journals 1. Revisiting Hua-Marcus-Bellman-Ando inequalities on contractive matrices, with C. Xu and Z. Xu, Lin. Alg. Appl. in press. 2. On the Bohr inequality of operators, J. of Math. Anal. Appl. 333(2007) Gersgorin type theorems for quaternionic matrices, Lin. Alg. Appl. 424(2007) Relative perturbation bounds for the eigenvalues of diagonalizable and singular matrices Application of perturbation theory for simple invariant subspaces, with Y. Wei, X. Li, F. Bu, Linear Algebra Appl. Vol. 419, pp , Eigenvalue inequalities for matrix product, with Q. Zhang, IEEE Trans. Auto. Contr., Vol. 51, No. 9, pp , Sept., 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 , Dec Matrix Inequalities by Means of Embedding, E. J. of Linear Algebra (International Linear Algebra Society), with T-G Lei and C-W Woo, Vol. 11, pp , Matrix Identity on the Schur Complement, Linear & Multilinear Algebra, Vol 52, No. 5, pp , The Schur Complements of Generalized Doubly Diagonally Dominant Matrices, with J. Liu, Y. Huang, Linear Algebra and its Applications, Vol. 378 (2004) On the Schur Complement of Diagonally Dominant Matrices, with Lei, Woo, Liu, SIAM Proceedings on Applied Linear Algebra Conference, Williamsburg, CP13, July Block Matrix Techniques and Matrix Inequalities, Numerical Mathematics, with S. Tang, Vol. 12, Supplement, pp , May 2003, Proceedings of the 5th China Matrix Theory and Its Applications - International Congress of Mathematicians (ICM) Satellite Conference, May Matrix Inequalities by Means of Block Matrices, Mathematical Inequalities and Applications, Vol. 4, Number 4, pp , October Jordan Canonical Form of a Partitioned Complex Matrix and Its Applications to Real Quaternion Matrices, with Y. Wei, Communications in Algebra, 29(6) (2001) 14. Equivalence of the Wielandt inequality and the Kantorovich inequality, Linear and Multilinear Algebra, Vol. 48m pp , Schur Complements and Matrix Inequalities in Löwner Ordering, Linear Algebra and Its Applications, Vol. 321, pp ,

2 16. Equivalence of a matrix product to the Kronecker product, with Y. Wei, Hadronic J. Supplement, 15, pp , On the Hadamard Product of Inverse M-matrices, with B-Y Wang and X. Zhang, Linear Algebra and Its Applications, Vol. 305, pp , Some Inequalities on Generalized Schur Complements, with B-Y Wang and X. Zhang, Linear Algebra and Its Applications, Vol (1999), pp Some Inequalities for Sum and Product of positive Semidefinite Matrices, with B-Y Wang and B-Y Xi, Linear Algebra and Its Applications, 293(1999), pp An Analog of Hua s Determinantal Inequality, with B-Y Wang, Hunan Annals of Mathematics (China), Vol. 18, No. 3, pp. 5 6, On the Precise Number of (0,1)-Matrices in A(R, S), with B-Y Wang, Discrete Mathematics, Vol. 187, pp , On Normal Matrices of Zeros and Ones with Fixed Row Sum, with B-Y Wang, Linear Algebra and Its Applications, Vol. 275/276, pp , On 0-1 Symmetric and Normal Matrices, with B-Y Wang, J. of Math Research and Exposition (China), Vol. 18, No. 2, pp , May, Schur Complements and Matrix Inequalities of Hadamard Products, with B-Y Wang, Linear and Multilinear Algebra, Vol. 43, pp , Norm Hull of Vectors and Matrices, with C-K Li and N-K Tsing, Linear Algebra and Its Applications, Vol. 257:1 27, Sign Patterns of Nonnegative Normal Matrices, with Z. Li and F. Hall, Linear Algebra and Its Applications, Vol. 254: , Quaternions and Matrices of Quaternions, Linear Algebra and Its Applications, Vol. 251:21 57, The Generalized Numerical Range with Completely Symmetric Function, with T-G Lei, Acta Mathematica Sinica, Vol. 39, No. 5, pp , Words and Normality of Matrices, with B-Y Wang, Linear and Multilinear Algebra, Vol. 40, No. 2: , An Operator Inequality and Matrix Normality, with Charles R Johnson, Linear Algebra and Its Application, Vol. 240, No. 1 3, pp , 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 , On Numerical Range of Normal Matrices of Quaternions, Journal of Mathematical and Physical Sciences, Vol. 29, No. 6, pp , Erratum Robison-Taussky inequality, with C. R. Johnson, Linear and Multilinear Algebra, Vol. 38, No. 3, p. 281,

3 34. A Trace Inequality for Unitary Matrices, with B-Y Wang, The American Mathematical Monthly, Vol. 101, Number 5, pp , Numerical Ranges of Normal Matrices of Quaternions, with W. So and R. C. Thompson, Linear and Multilinear Algebra, Vol. 37, pp , Two Conjectures on Permanents, with G. Liang and W. So, Linear Algebra and its Applications, Vol. 197&198, pp , A Majorization Conjecture for Hadamard Products and Compound Matrices, Linear and Multilinear Algebra, Vol. 33, No. 4, p , Some Inequalities for the Eigenvalues of the Product of Positive Semi-definite Hermitian Matrices, with Bo-Ying Wang, Linear Algebra and Its Applications, Vol. 160, pp , Notes on Hadamard Products of Matrices, Linear and Multilinear Algebra, Vol. 25, pp , Some Identities of Permanents, Mathematics in Practice and Theory (China), No. 1, pp , Another Proof of a Singular Value Inequality Concerning Hadamard Products of Matrices, Linear and Multilinear Algebra, Vol. 22, pp , Solution to a Conjecture of Marcus, Kidman, and Sandy, J. of Beijing Normal University (Nature Sci.), Supplement No. 2, pp , On Eigenvalue and Singular Value Inequalities for Matrix Product, J. of Beijing Normal University (Nature Sci.), No. 3, pp. 1 4, On the Best Euclidean Fit to a Distance Matrix, J. of Beijing Normal University (Nature Sci.), No. 4, pp , Some Notes on The inequality of Hermitian Square Matrices, Mathematics in Practice and Theory (China), No. 2, pp , Theses 46. Permanent Inequalities and Quaternion Matrices, Ph.D. Dissertation, University of California, Santa Barbara, May Inequalities Concerning Hadamard Products of Matrices, The thesis for M.S. Degree, April (Collected in Best Thesis Collection of Beijing Normal University 1997) Books 48. Counterexamples in Matrix Analysis, manuscript, 200+ pages. 49. The Schur Complement and Its Applications, Editor, Springer, New York,

4 50. Matrix Theory: Basic Results and Techniques, Springer, New York, Linear Algebra: Challenging Problems for Students, Johns Hopkins University Press, Baltimore, 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, Problems posed or solved, etc. - Excluding referee reports or math reviews 53. Eigenvalues and Eigenvectors of a Particular Tridiagonal Matrix, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 31, p. 43, Oct., Solution to the problem proposed by J. Gross and G. Trenkler, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 30, p. 25, April, Report on the China Matrix Meeting - ICM Satellite Meeting, with E. Jiang, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 29, p. 8, Oct., Florida Matrix Analysis Conference Announcement, with C-K Li, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 29, p. 12, Oct., Solution to the problem proposed by Y. Wei and F. Zhang, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 29, p. 33, Oct., Solution to the problem proposed by C. R. Johnson, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 28, p. 31, April, Problem 28-9: A Relative Perturbation Bound, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 28, p. 35, April, Problem 28-10: Inequalities involving Square Roots, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 28, p. 35, April, Solution to the problem proposed by J. Gross and S. Troschke, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 26, p. 4, April, Solution to the problem proposed by S. Drury, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 26, p. 12, April, Problem 25-8: Several Matrix Orderings involving Matrix Geometric and Arithmetic Means, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 25, p. 17, Oct., Problem 24-6: Rank of a Principal Submatrix, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 24, p. 17, April, Problem 24-7: Partitioned Positive Semidefinite Matrices, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 24, p. 17, April, Problem 24-8: An Inequality involving Hadamard Products, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 24, p. 17, April,

5 67. 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, Solution to the Problem proposed by L. Elsner, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 22, p. 27, April, Solution to the Problem proposed by G. Trenkler, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 22, p. 30, April, Report on Chinese matrix Conference, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 21, p. 16, Matrix Similarity, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 20, Problem 20 5, p. 32, Nonnegative Definiteness and Square Roots, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 20, Problem 20-6, p. 32, Book Review: Nonnegative Matrices and Applications by R. Bapat and T. Raghavan, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 20, p. 2, April, Solution to the Problem proposed by F. Zhang, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 23, p. 27, Oct., On a Characterization Associated with the Matrix Arithmetic and Geometric Means: Solution to , with C-K Li, International Linear Algebra Society Bulletin IMAGE, No. 18, p. 31, Proposed Problem #10513: Positivity of a Block Matrix, The American Mathematical Monthly, p. 267, June, Solution to a problem in Econometric Theory, Vol. 12, pp , with G. P. H. Styan, Robert Charles Thompson, International Linear Algebra Society Bulletin IMAGE, No. 16, pp. 5-6, A Determinantal Inequality, International Linear Algebra Society (ILAS) Bulletin IM- AGE, No. 16, Problem 16-1, p. 32, A Hadamard Product Inequality, International Linear Algebra Society (ILAS) Bulletin IMAGE, No. 16, Problem 16-2, p. 32, Presentations 1. Contributed talk: Hua s Determinantal Inequality and Beyond, July 16-20, 2007, Minisymposium on Schur Complement and Applications, the 14th ILAS Meeting, Shanghai University, Shanghai, China. 2. Invited talks: Two New Proofs for Hua s Matrix Inequalities, Shenyang Agricultural University (June, 2007), Shenyang; Zhejiang Forestry University (7/23/07), Hangzhou; Fudan University (7/24/07), Shanghai, China. 5

6 3. Invited Series talks: Quaternions and Matrices of Quaternions, July 9-13, 2007, Beijing Normal University, Beijing, China. 4. Invited talk: Hua s Inequalities and Schur Complements, June 19, 2007, Northeast University, Shenyang, China. 5. Contributed talk: Hua s matrix equality and Schur complement, March 24, 2007, Auburn University, R. C. Thompson Matrix Conference. 6. Contributed talk: Some matrix and operator inequalities involving A, July 22, 2006, Amsterdam, 13th International Linear Algebra Society Conference. 7. Contributed talk: Why left and right spectral radii are different, July 16, 2006, Bremen University, Germany. 8. Invited talk: Absolute value of matrices and operators, June 9, Beijing Normal University, Beijing, China. 9. Invited talk: Matrix eigenvalue inequalities, June 5, 2006, Institute of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China. 10. Contributed talk: Teaching Linear Algebra as a Tutorial, March 25, 2006, Drexel University, Philadelphia. 11. Invited talk: Research on quaternionic matrices: A survey, July 4, 2005, Northeastern University, Shenyang, China. 12. Contributed talk: Left eigenvalue problems of quaternionic matrices, The 1st International Workshop on Matrix Analysis, June 9-10, 2005, Beijing. 13. Contributed talk: Disc separation of the Schur complement, Nov. 16, 2004, San Jose, California. 14. Contributed talk: The Schur complement, April 17, 2004, University of California at Santa Barbara. 15. Contributed talk: On the Schur Complement of Diagonally Dominant Matrices, SIAM Meeting on Applied Linear Algebra, July 15-20, 2003, Williamsburg. 16. Invited plenary Talk: Block Matrix Techniques, ICM Conference Shanghai satellite meeting on Matrix Theory, Invited plenary speaker, August 14-18, 2002, Shanghai, China. 17. Contributed talk: Matrix Inequalities by Embedding, Workshop on Numerical Range and Numerical Radii, June 7-8, 2002, Auburn, AL. 18. Invited Talk: Sums and Products of Positive Things Are Positive, Plenary, August 1-3, 2001, Voorburg, Netherlands. 19. Invited talk: Matrix Inequalities, July 2000, Beijing Normal University, Northeastern University, Fudan University, China. 20. Contributed talk: Tournament Matrices, Math Seminar, Nov. 10, 1999, Nova Southeastern University, Fort Lauderdale. 6

7 21. Contributed talk: Quaternion Matrices, Math Seminar, Nov. 3, 1999, Nova Southeastern University, Fort Lauderdale. 22. Contributed talk: A Matrix Inequality and a Rank Identity, Minisymposium, Special session for R. C. Thompson, 8th International Linear Algebra Society (ILAS) Conference, July 19-22, 1999, Barcelona, Spain. 23. Contributed talk: A Matrix Inequality and Its Beautiful Proof, Plenary, 7th International Conference on Matrices and Statistics, Dec , 1998, Fort Lauderdale. 24. Invited talk: Numerical Range of Quaternion Matrices: A survey, Plenary, 3rd Chinese Conference on Matrices and Applications, August 8-13, 1998, Zhang Jiajie, China. 25. Invited talk: Hua s Inequality: New proofs, Generalizations, and Analogs, July 1998, Beijing University and Northeastern University, China. 26. Contributed talk: Matrix Inequalities on Schur Complements, 7th International Linear Algebra Society (ILAS) Conference (Session Chair of Core Linear Algebra I), June 3-6, 1998, University of Wisconsin-Madison. 27. Invited talk: Schur Complements, Nov. 27, 1997, McGill University, Montreal, Canada. 28. Contributed talk: Contraction Matrices as the Convex Combinations of Unitary Matrices, Nov. 20, 1997, Math Seminar, Nova Southeastern University, Fort Lauderdale, Florida. 29. Contributed talk: Jordan Canonical Forms of Quaternion Matrices, Nov. 15, 1997, 11th Southern California Matrix Conference, Northridge, California. 30. Contributed talk: Normal Matrices of Zero and One Entries, August 14-17, 1996, The 6th International Linear Algebra Conference, Chemnitz, Germany. 31. Contributed talk: Words and Matrix Normality, August 16, 1995, The 5th International Linear Algebra Conference, Atlanta, Georgia. 32. Contributed talk: An Operator Inequality and Matrix Normality, November 12, 1994, University of Utah, Salt Lake City, Utah. 33. Contributed talk: Homotopy and Linear Algebra, October, 1994, Nova Southeastern University, Fort Lauderdale, Florida. 34. Invited talk: Linear Algebra Research Problems, August, 1994, Institute of Mathematics, The Chinese Academy of Sciences, Beijing, China. 35. Invited talk: An Operator Inequality, August, 1994, Beijing Normal University, Beijing, China. 36. Contributed talk: Gems in Linear Algebra (a series), October, 1993, Nova University, Fort Lauderdale, Florida. 37. Contributed talk: Trace and Eigenvalue Inequalities, California Matrix Conference, November 6, 1993, San Jose, California. 38. Contributed talk: Everything about Matrices of Quaternions, the 99th AMS & MAA joint meeting, January, 1993, San Antonio, Texas. 7

8 39. Contributed talk: Generalized and joint Spectral Radii, December, 1992, College of William and Mary, Virginia. 40. Contributed talk: Permanent Inequalities, Sept. 1, 1992, The College of William and Mary, Virginia. 41. Contributed talk: Maximizing Matrices, 2nd International Linear Algebra Society Conference, August, 1992, Lisbon, Portugal. 42. Invited talk: Permanents, Hadamard Products and Open Problems, Sept. 1991, McGill University, Montreal, Canada. 43. Contributed talk: On a Theorem in Ring Theory, The 3th National Algebra Conference, 1988, Xian, China. 44. Contributed talk: Distance Matrices, The 4th conference on Numerical Analysis in China, 1987, Dalian, China. 8