Matrix Inequalities Lecture Notes In Mathematics Pdf

Xingzhi Zhan

Professor of Mathematics

Office: Room 323, Math. Building

Tel: 86-21-54342646-323

Fax: 86-21-54342609

Email: zhan@math.ecnu.edu.cn

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

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,
0-1 matrices, matrix inequalities, operator monotone functions, unitary (orthogonal) orbits,
completion of partial matrices

Publications

Books
- Matrix Inequalities, Lecture Notes in Mathematics 1790, Springer-Verlag, 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, 255--258
- Computing the extremal positive definite solutions of a matrix equation,
  SIAM J. Sci. Comput. 17 (1996), no. 5, 1167--1174
- (with J. Xie) On the matrix equation X+A^TX^{-1}A=I,
  Linear Algebra Appl. 247 (1996), 337--345
- Inequalities for the singular values of Hadamard products,
  SIAM J. Matrix Anal. Appl. 18 (1997), no. 4, 1093--1095
- (with E. Jiang) Lower bounds for the spread of a Hermitian matrix,
  Linear Algebra Appl. 256 (1997), 153--163
- Inequalities involving Hadamard products and unitarily invariant norms,
  Adv. in Math. (China) 27 (1998), no. 5, 416--422
- Inequalities for unitarily invariant norms,
  SIAM J. Matrix Anal. Appl. 20 (1998), no. 2, 466--470
- (with T. Ando) Norm inequalities related to operator monotone functions,
  Math. Ann. 315 (1999), no. 4, 771--780
- (with R. A. Horn) Inequalities for C-S seminorms and Lieb functions,
  Linear Algebra Appl. 291 (1999), 103--113
- Norm inequalities for Cartesian decompositions,
  Linear Algebra Appl. 286 (1999), 297--301
- Singular values of differences of positive semidefinite matrices,
  SIAM J. Matrix Anal. Appl. 22 (2000), no.3, 819--823
- Some research problems on the Hadamard product and singular values of matrices,
  Linear and Multilinear Algebra 47 (2000), no.2, 191--194
- (with R. Bhatia) Compact operators whose real and imaginary parts are positive,
  Proc. Amer. Math. Soc. 129 (2001), no.8, 2277--2281
- Linear preservers that permute the entries of a matrix,
  Amer. Math. Monthly 108 (2001), no.7, 643--645
- Span of the orthogonal orbit of real matrices,
  Linear and Multilinear Algebra 49 (2001), 337--346
- (with F. Ding) On the unitary orbit of complex matrices,
  SIAM J. Matrix Anal. Appl. 23 (2001) no.2, 511--516
- (with F. Hiai) Inequalities involving unitarily invariant norms and operator monotone functions,
  Linear Algebra Appl. 341(2002), 151--169
- The sharp Rado theorem for majorizations,
  Amer. Math. Monthly 110(2003), 152--153
- (with R. Bhatia) Norm inequalities for operators with positive real part,
  J. Operator Theory 50(2003), 67--76
- On some matrix inequalities,
  Linear Algebra Appl. 376(2004), 299--303
- (with F. Hiai) Submultiplicativity vs subadditivity for unitarily invariant norms,
  Linear Algebra Appl. 377(2004), 155--164
- On singular numbers of tau-measurable operators,
  J. of Shanghai University, Special issue dedicated to the 70th birthday of Professor Erxiong Jiang, 8(2004), no.4, 444--447
- (with Q. Hu and Y. Li) Possible numbers of ones in 0-1 matrices with a given rank,
  Linear and Multilinear Algebra 53(2005), no.6, 435--443 pdf file
- Formulae for sums of consecutive square roots,
  Math. Intelligencer 27(2005), no.4, 4--5 pdf file
- Extremal eigenvalues of real symmetric matrices with entries in an interval ,
  SIAM J. Matrix Anal. Appl. 27(2006), no. 3, 851--860 pdf file
- Completion of a partial integral matrix to a unimodular matrix,
  Linear Algebra Appl. 414(2006), 373--377 pdf file
- (with L. Qiu) On the span of Hadamard products of vectors,
  Linear Algebra Appl. 422(2007), 304--307 pdf file
- Extremal numbers of positive entries of imprimitive nonnegative matrices,
  Linear Algebra Appl. 424(2007), 132--138 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, 367--382 pdf file
- (with R.A. Brualdi and P. Pei) An extremal sparsity property of the Jordan canonical form,
  Linear Algebra Appl. 429(2008), 2367--2372 pdf file
- (with R.A. Brualdi and Z. Huang) Singular, nonsingular, and bounded rank completions of ACI-matrices,
  Linear Algebra Appl. 433(2010), 1452--1462 pdf file
- (with Z. Huang) Digraphs that have at most one walk of a given length with the same endpoints,
  Discrete Math., 311(2011), 70--79. pdf file
- (with Z. Huang) ACI-matrices all of whose completions have the same rank,
  Linear Algebra Appl., 434 (2011), 1956--1967. pdf file
- (with Z. Huang) Extremal digraphs whose walks with the same initial and terminal vertices have distinct lengths,
  Discrete Math., 312(2012), 2203--2213. pdf file
- (with Z. Huang) Partial matrices all of whose completions have the same spectrum,
  Linear Algebra Appl., 436(2012), 3061--3064. pdf file
- (with C. Ma) Extremal sparsity of the companion matrix of a polynomial,
  Linear Algebra Appl., 438(2013), 621--625. pdf file
- (with C. Ma) Inverse invariant zero�Cnonzero patterns,
  Linear Algebra Appl., 443(2014), 184--190. pdf file
- (with Z. Huang) Nonsymmetric normal entry patterns with the maximum number of distinct indeterminates,
  Linear Algebra Appl., 485(2015), 359--371. pdf file
- (with S. Kirkland and P. Qiao) Algebraically positive matrices,
  Linear Algebra Appl., 504(2016), 14--26. pdf file
- (with P. Qiao) On vertex types of graphs,
  Graph Combin., 34(2018), 889--900. pdf file
- (with P. Qiao) The maximum girth and minimum circumference of graphs with prescribed radius and diameter,
  Discrete Math., 341(2018), 2827--2830. pdf file
- (with P. Qiao) The largest graphs with given order and diameter: A simple proof,
  Graphs Combin., 35(2019), 1715--1716. pdf file
- (with P. Qiao) The minimum number of Hamilton cycles in a hamiltonian threshold graph of a prescribed order,
  J. Graph Theory, 93(2020), 222--229. pdf file
- (with P. Qiao) Pairs of a tree and a nontree graph with the same status sequence,
  Discrete Math., 343(2020), no.2, article number 111662. 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 16-18, 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 17-20, 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 26-29, 2005
- Submultiplicativity vs subadditivity for unitarily invariant norms,
  The 6th conference of China matrix theory and applications, Heilongjiang University, Harbin, China, July 18-20, 2004
- On the unitary orbit of complex matrices,
  The 5th conference of China matrix theory and applications, Shanghai University, Shanghai, China, August 14-18, 2002
- Inequalities for unitarily invariant norms,
  The 3rd conference of China matrix theory and applications, Zhang Jia Jie, China, August 8-13, 1998
Invited 45-minute talk
- Open Problems in Matrix Theory, pdf file
  The 4th International Congress of Chinese Mathematicians, Zhejiang University, Hangzhou, China, Dec. 17-22, 2007
Invited 40-minute talk
- Sparsity of matrix canonical forms, pdf file
  The 6th Asian Mathematical Conference, Busan, Korea, June 30-July 4, 2013
Invited ILAS lecture
- Unsolved Matrix Problems, pdf file
  Advanced Workshop on Trends and Developments in Linear Algebra, ICTP, Trieste, Italy, July 6-10, 2009
Invited 30-minute 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 22-25, 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 24-28, 2012
- Extremal sparsity of the companion matrix of a polynomial, pdf file
  International Workshop on Matrices and Operators, Beijing Normal University, Beijing, July 15-18, 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)