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Che Man CHENG, Raymond鄭智文 Associate Professor Associate Head of Department of Mathematics (MAT) |
Academic Qualification
- PhD (Mathematics), The University of Hong Kong, Hong Kong (1991)
- B.Sc. (Mathematics), The University of Hong Kong, Hong Kong (1987)
Working Experience
2016- | Associate Head of Department of Mathematics, FST, UM |
2000- | Associate professor, FST, UM |
2002-2005, | Head of Department of Mathematics, FST, UM |
1999-2001, | Member of the Management Committee of Faculty of Education, UM |
1997-2002, | Coordinator of Mathematics program, FST, UM |
1992-2000, | Assistant professor, FST, UM |
Teaching
B.Sc. Courses
- Abstract Algebra I (EDUC350)
- Abstract Algebra II (EDUC351)
- Calculus I (MATB110)
- Calculus II (MATB120)
- Complex Analysis (EDUC354)
- Linear Algebra (MATH103)
- Operations Research (MATB226)
- Operations Research I (SFTW122)
- Operational Research (EDUC413)
- Quantitative Reasoning for Science and Technology (GEST1004)
- Real Analysis I (EDUC204)
- Mathematical Analysis I (MATH101)
- Mathematical Analysis II (MATH102)
- Mathematical Analysis III (MATB350)
M.Sc. Courses
- Algebra (IMMT110)
- Matrix Analysis (IMMT125)
- Matrix Analysis (IMAT008)
Research
Research Interests
- Matrix theory, including numerical ranges, eigenvalues and singular values, norms of commutators, and Hurwitz matrix equations
Selected Publications
- C.-M. Cheng, A note on interlacing polynomial, Southeast Asian Bull. Math. 14 (1990), 25-26.
- C.-M. Cheng, Two results on C-congruence numerical radii, Tamkang J. Math. 21 (1990), 59-64.
- C.-M. Cheng, An approximation problem with respect to symmetric gauge functions with applications to matrix spaces, Linear and Multilinear Algebra29 (1991), 169-180.
- Y.-H. Au-Yeung, C. M. Cheng, Permutation matrices whose convex combinations are orthostochastic, Linear Algebra Appl. 150 (1991), 243-253.
- C.-M. Cheng, Independence of eigenvalues and independence of singular values of submatrices, Linear Algebra Appl. 166 (1992), 115-129.
- C.-M. Cheng, Cases of equality for a singular value inequality of the Hadamard product, Linear Algebra Appl. 177 (1992), 209-231.
- Y.-H. Au-Yeung, C.-M. Cheng, Two formulas for the Radon-Hurwitz number, Linear and Multilinear Algebra34 (1993), 59-65.
- C.-M. Cheng, On the decomposable numerical range of λI-N, Linear and Multilinear Algebra37 (1994), 197-205.
- C.-M. Cheng, C.-K. Li, Some geometrical properties of the decomposable numerical range, Linear and Multilinear Algebra37 (1994), 207-212.
- C.-M. Cheng, On principal sections of a pair of forms, Proc. Amer. Math. Soc. 123 (1995), 2949-2954.
- C.-M. Cheng, C. K. Li, On the Hu-Hurley-Tam conjecture concerning the generalized numerical range, Linear Algebra Appl. 305 (2000), 87-97.
- C.-M. Cheng, R. A. Horn, C.-K. Li, Inequalities and equalities for the Cartesian decomposition of complex matrices, Linear Algebra Appl. 341 (2002), 219-237.
- C.-M. Cheng, X-Q Jin, Some stability properties of T. Chan’s preconditioner, Linear Algebra Appl.395 (2005), 361-365.
- C.-M. Cheng, X.-Q. Jin, Y-M Wei, Stability properties of superoptimal preconditioner from numerical range, Numer. Linear Algebra Appl. 13 (2006), 513-521.
- Y.-H. Au-Yeung, C.-M. Cheng, On the pure imaginary quaternionic solutions of the Hurwitz matrix equations, Linear Algebra Appl. 419 (2006), 630-642.
- C.-M. Cheng, X.-Q. Jin, V.-K. Sin, Stability properties of T. Chan’s preconditioner from numerical range, Numerical Mathematics: A Journal of Chinese Universities (English series) 16 (2007), 28-36.
- C. M. Cheng, X.-Q. Jin, S.-W. Vong, W. Wang, A note on spectra of optimal and superoptimal preconditioned matrices, Linear Algebra Appl. 422 (2007), 482-485.
- C.-M. Cheng, I.-C. Law, S.-I Leong, Eigenvalue equalities for ordinary and Hadamard products of powers of positive semidefinite matrices, Linear Algebra Appl. 422 (2007), 771-787.
- C.-M. Cheng, K.-L. Cheok, I.-T. Leong, 3×3 pure imaginary quaternionic solutions of the Hurwitz matrix equations, Linear and Multilinear Algebra 58 (2010), 863-874.
- C.-M. Cheng, S.-W. Vong, D. Wenzel, Commutators with maximal Frobenius norm, Linear Algebra Appl. 432 (2010), 292-306.
- K.-S. Fong, C.-M. Cheng, I.-K. Lok, Another unitarily invariant norm attaining the minimum norm bound for commutators, Linear Algebra Appl. 433 (2010), 1793-1797.
- C.-M. Cheng, K.-S. Fong, I.-K. Lok, Another proof for commutators with maximal Frobenius norm, Recent Advances in Scientific Computing and Matrix Analysis, p. 9-14, Editors: X.-Q. Jin, H.-W. Sun, S.-W. Vong, International Press, 2011.
- K.-S. Fong, I.-K. Lok, C.-M. Cheng, A note on the norm of commutator and the norm of XY-YX^T, Linear Algebra Appl. 435 (2011), 1191-1201.
- C.-M. Cheng, K.-S. Fong, W.-F. Lei, On some norm inequalities involving the commutator and XY-YX^T, Linear Algebra Appl. 438 (2013), 2793-2807.
- C.-M. Cheng, Y. Gao, A note on numerical range and product of matrices, Linear Algebra Appl. 438 (2013), 3139-3143. Corrigendum, Linear Algebra Appl. 459 (2014), 622-624.
- C.-M. Cheng, X.-Q. Jin, Matrix decomposition, Encyclopedia of Social Network Analysis and Mining, p. 880-890, Springer Science and Business Media, New York, 2014. ISBN 978-1-4614-6169-2
- R. Alizadeh, M. B. Asadi, C.-M. Cheng, W. Hong, C.-K. Li, Spectral radius, numerical radius, and the product of operators, J. Math. Anal. Appl. 423 (2015), 639-645.
- C.-M. Cheng, X.-Q. Jin, S.-W. Vong, A survey on the Böttcher-Wenzel conjecture and related problems, Oper. Matrices, 9 (2015), 659-673.
- C.-M. Cheng, C. Lei, On Schatten p-norms of commutators, Linear Algebra Appl. 484 (2015), 409-434.
- C.-M. Cheng, Y. Liang, Some sharp bounds for the commutator of real matrices, Linear Algebra Appl. 521 (2017), 263-282.
- Z.-J. Xie, C.-M. Cheng, X. Jin, Some norm inequalities for commutators of contracted tensor products, Linear Algebra Appl. 540 (2018), 244-256.
- C.-M. Cheng, Y. Liang, Singular values, eigenvalues and diagonal elements of the commutator of 2×2 rank one matrices, Electron. J. Linear Algebra, 36 (2020), 1-20.
- C.-M. Cheng, R. Jiao, Proof of Wenzel’s conjecture concerning singular values of the commutator of rank one matrices, Linear Algebra Appl. 592 (2020), 165-174.
Contact Details
Faculty of Science and Technology
University of Macau, E11
Avenida da Universidade, Taipa,
Macau, China
Room: E11-3065
Telephone: (853) 8822-4457
Fax: (853) 8822-2426
Email: fstcmc