
Xingzhi Zhan 
Professor of Mathematics

Office: Room 323, Math. Building

Tel: 862154342646323

Fax: 862154342609

Email: zhan@math.ecnu.edu.cn

Mailing:
Department of Mathematics, East China Normal University,
Shanghai 200241, China





CV
 Education
 B.S: Jingzhou Normal College, July 1986
 M.S: East China Normal University, July 1993
 Ph.D: Fudan University, July 1996
 Working Experiences
 1996.07  2000.02,
Peking University, Beijing, Postdoctoral Fellow, Associate Professor
 2000.02  2002.02,
Tohoku University, Sendai, Japan, JSPS Postdoctoral Fellow
 2002.02  2003.02,
Peking University, Beijing, Associate Professor
 2003.02  2005.10,
East China Normal University, Shanghai, Professor
 2005.10  2006.08,
The Hong Kong University of Science and Technology,
Hong Kong, Visiting Scholar
 2006.08 
East China Normal University, Shanghai, Professor



Research Interests
 Graph Theory:
Longest cycle, longest path, spanning tree, distance,
diameter, radius, center, periphery,
independence number,
domination number, connectivity, chromatic number
 Matrix Theory:
Singular values, eigenvalues, unitarily invariant norms,
nonnegative matrices, sign patterns,
01 matrices, matrix inequalities,
operator monotone functions, unitary (orthogonal) orbits,
completion of partial matrices



Publications
 Books
 Matrix Inequalities,
Lecture Notes in Mathematics 1790,
SpringerVerlag, Berlin, 2002.
Cover
 Matrix Theory,
Graduate Studies in Mathematics 147,
American Mathematical Society, Providence, 2013.
Cover
 Papers

On a question of P. R. Halmos,
Linear and Multilinear Algebra 39 (1995), no.3, 255258

Computing the extremal positive definite solutions of a matrix equation,
SIAM J. Sci. Comput. 17 (1996), no. 5, 11671174

(with J. Xie) On the matrix equation X+A^TX^{1}A=I,
Linear Algebra Appl. 247 (1996), 337345

Inequalities for the singular values of Hadamard products,
SIAM J. Matrix Anal. Appl. 18 (1997), no. 4, 10931095

(with E. Jiang) Lower bounds for the spread of a Hermitian matrix,
Linear Algebra Appl. 256 (1997), 153163

Inequalities involving Hadamard products and unitarily invariant norms,
Adv. in Math. (China) 27 (1998), no. 5, 416422

Inequalities for unitarily invariant norms,
SIAM J. Matrix Anal. Appl. 20 (1998), no. 2, 466470

(with T. Ando) Norm inequalities related to operator monotone functions,
Math. Ann. 315 (1999), no. 4, 771780

(with R. A. Horn) Inequalities for CS seminorms and Lieb functions,
Linear Algebra Appl. 291 (1999), 103113

Norm inequalities for Cartesian decompositions,
Linear Algebra Appl. 286 (1999), 297301

Singular values of differences of positive semidefinite matrices,
SIAM J. Matrix Anal. Appl. 22 (2000), no.3, 819823

Some research problems on the Hadamard product and singular values of matrices,
Linear and Multilinear Algebra 47 (2000), no.2, 191194

(with R. Bhatia) Compact operators whose real and imaginary parts are positive,
Proc. Amer. Math. Soc. 129 (2001), no.8, 22772281

Linear preservers that permute the entries of a matrix,
Amer. Math. Monthly 108 (2001), no.7, 643645

Span of the orthogonal orbit of real matrices,
Linear and Multilinear Algebra 49 (2001), 337346

(with F. Ding) On the unitary orbit of complex matrices,
SIAM J. Matrix Anal. Appl. 23 (2001) no.2, 511516

(with F. Hiai) Inequalities involving unitarily invariant norms and operator monotone functions,
Linear Algebra Appl. 341(2002), 151169

The sharp Rado theorem for majorizations,
Amer. Math. Monthly 110(2003), 152153

(with R. Bhatia) Norm inequalities for operators with positive real part,
J. Operator Theory 50(2003), 6776

On some matrix inequalities,
Linear Algebra Appl. 376(2004), 299303

(with F. Hiai) Submultiplicativity vs subadditivity for unitarily invariant norms,
Linear Algebra Appl. 377(2004), 155164

On singular numbers of taumeasurable operators,
J. of Shanghai University, Special issue dedicated to the 70th birthday of Professor Erxiong Jiang, 8(2004), no.4, 444447

(with Q. Hu and Y. Li) Possible numbers of ones in 01 matrices with a given rank,
Linear and Multilinear Algebra 53(2005), no.6, 435443
pdf file

Formulae for sums of consecutive square roots,
Math. Intelligencer 27(2005), no.4, 45
pdf file

Extremal eigenvalues of real symmetric matrices with entries in an interval ,
SIAM J. Matrix Anal. Appl. 27(2006), no. 3, 851860
pdf file

Completion of a partial integral matrix to a unimodular matrix,
Linear Algebra Appl. 414(2006), 373377
pdf file

(with L. Qiu) On the span of Hadamard products of vectors,
Linear Algebra Appl. 422(2007), 304307
pdf file

Extremal numbers of positive entries of imprimitive nonnegative matrices,
Linear Algebra Appl. 424(2007), 132138
pdf file

Open problems in matrix theory,
in
Proceedings of the 4th International Congress of Chinese Mathematicians, Vol. I, edited by L. Ji, K. Liu, L. Yang and S.T. Yau, Higher Education Press, Beijing, 2008, 367382
pdf file

(with R.A. Brualdi and P. Pei) An extremal sparsity property of the Jordan canonical form,
Linear Algebra Appl. 429(2008), 23672372
pdf file

(with R.A. Brualdi and Z. Huang)
Singular, nonsingular, and bounded rank completions of ACImatrices,
Linear Algebra Appl. 433(2010), 14521462
pdf file

(with Z. Huang)
Digraphs that have at most one walk of a given length with the same endpoints,
Discrete Math., 311(2011), 7079.
pdf file

(with Z. Huang)
ACImatrices all of whose completions have the same rank,
Linear Algebra Appl., 434 (2011), 19561967.
pdf file

(with Z. Huang)
Extremal digraphs whose walks with the same initial
and terminal vertices have distinct lengths,
Discrete Math., 312(2012), 22032213.
pdf file

(with Z. Huang)
Partial matrices all of whose completions have the same spectrum,
Linear Algebra Appl., 436(2012), 30613064.
pdf file

(with C. Ma)
Extremal sparsity of the companion matrix of a polynomial,
Linear Algebra Appl., 438(2013), 621625.
pdf file

(with C. Ma)
Inverse invariant zero¨Cnonzero patterns,
Linear Algebra Appl., 443(2014), 184190.
pdf file

(with Z. Huang)
Nonsymmetric normal entry patterns with the maximum number of distinct indeterminates,
Linear Algebra Appl., 485(2015), 359371.
pdf file
 (with S. Kirkland and P. Qiao)
Algebraically positive matrices,
Linear Algebra Appl., 504(2016), 1426.
pdf file
 (with P. Qiao)
On vertex types of graphs,
Graph Combin., 34(2018), 889900.
pdf file
 (with P. Qiao)
The maximum girth and minimum circumference of graphs with prescribed radius and diameter,
Discrete Math., 341(2018), 28272830.
pdf file



Professional Service
 Linear Algebra and Its Applications,
Associate Editor (2007  )
 Linear and Multilinear Algebra,
Member of Editorial Board (2009  2013)
 Electronic Journal of Linear Algebra,
Associate Editor (2011  2013)



Invited Talks
 Invited plenary talks

Extremal sparsity property of the Jordan canonical form,
pdf file
The 8th conference of China matrix theory and applications,
Taiyuan Normal University, Taiyuan, China,
July 1618, 2008

On nonnegative imprimitive matrices,
pdf file
The 7th conference of China matrix theory and applications,
University of Electronic Science and Technology, Chengdu, China,
July 1720, 2006

Extremal eigenvalues of real symmetric matrices
with entries in an interval,
pdf file
The 12th conference of the International Linear Algebra Society,
University of Regina, Canada, June 2629, 2005

Submultiplicativity vs subadditivity for unitarily
invariant norms,
The 6th conference of China matrix theory and applications,
Heilongjiang University, Harbin, China, July 1820, 2004

On the unitary orbit of complex matrices,
The 5th conference of China matrix theory and applications,
Shanghai University, Shanghai, China, August 1418, 2002

Inequalities for unitarily invariant norms,
The 3rd conference of China matrix theory and applications,
Zhang Jia Jie, China, August 813, 1998
 Invited 45minute talk

Open Problems in Matrix Theory,
pdf file
The 4th International Congress of Chinese Mathematicians,
Zhejiang University, Hangzhou, China, Dec. 1722, 2007
 Invited 40minute talk

Sparsity of matrix canonical forms,
pdf file
The 6th Asian Mathematical Conference, Busan, Korea,
June 30July 4, 2013
 Invited ILAS lecture

Unsolved Matrix Problems,
pdf file
Advanced Workshop on Trends and Developments in Linear Algebra,
ICTP, Trieste, Italy, July 610, 2009
 Invited 30minute talk

Digraphs that have at most one walk of a given length with the same endpoints,
pdf file
The 4th National Conference on Combinatorial Mathematics and Graph Theory,
Xuzhou Normal University, Xuzhou, China, August 2225, 2010

Extremal digraphs whose walks with the same initial and terminal
vertices have distinct lengths,
pdf file
Workshop on Positive Matrices and Operators: Recent Developments and Advances,
Kyungpook National University, Daegu, Korea, June 2428, 2012

Extremal sparsity of the companion matrix of a polynomial,
pdf file
International Workshop on Matrices and Operators,
Beijing Normal University, Beijing, July 1518, 2013



Teaching
 Courses
 Spring semester 2016:
Linear Algebra II (undergraduate),
Modern Graph Theory (graduate),
Combinatorics and Graph Theory (graduate),
Seminar on Structures of Graphs (graduates).
 Autumn semester 2016:
Matrix Theory (graduate),
Seminar on Cycles and Paths of Graphs
 Former PhD students
 Rong Huang (2008),
Maozhong Fang (2008),
Honglin Wu (2009),
Zejun Huang (2011),
Jin Zhong (2012),
Yun Zhang (2014),
Chao Ma (2014)



Hobbies
 Music, literature, table tennis, friendship, . . .



Last updated on August 18, 2016

