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

  1. Calculus I (MATB110)
  2. Calculus II (MATB120)
  3. Complex Analysis (EDUC354)
  4. Linear Algebra (MATH103)
  5. Operations Research (MATB226)
  6. Quantitative Reasoning for Science and Technology (GEST1004)
  7. Mathematical Analysis I (MATH101)
  8. Mathematical Analysis II (MATH102)
  9. Mathematical Analysis III (MATB350)

M.Sc. Courses

  1. Matrix Analysis (MATH7008)

Research

Research Interests

  • Matrix theory, including numerical ranges, eigenvalues and singular values, norms of commutators, and Hurwitz matrix equations

Publications

  1. C.-M. Cheng, A note on interlacing polynomial, Southeast Asian Bull. Math. 14 (1990), 25-26.
  2. C.-M. Cheng, Two results on C-congruence numerical radii, Tamkang J. Math. 21 (1990), 59-64.
  3. C.-M. Cheng, An approximation problem with respect to symmetric gauge functions with applications to matrix spaces, Linear and Multilinear Algebra 29 (1991), 169-180.
  4. Y.-H. Au-Yeung, C. M. Cheng, Permutation matrices whose convex combinations are orthostochastic, Linear Algebra Appl. 150 (1991), 243-253.
  5. C.-M. Cheng, Independence of eigenvalues and independence of singular values of submatrices, Linear Algebra Appl. 166 (1992), 115-129.
  6. C.-M. Cheng, Cases of equality for a singular value inequality of the Hadamard product, Linear Algebra Appl. 177 (1992), 209-231.
  7. Y.-H. Au-Yeung, C.-M. Cheng, Two formulas for the Radon-Hurwitz number, Linear and Multilinear Algebra 34 (1993), 59-65.
  8. C.-M. Cheng, On the decomposable numerical range of λI-N, Linear and Multilinear Algebra 37 (1994), 197-205.
  9. C.-M. Cheng, C.-K. Li, Some geometrical properties of the decomposable numerical range, Linear and Multilinear Algebra 37 (1994), 207-212.
  10. C.-M. Cheng, On principal sections of a pair of forms, Proc. Amer. Math. Soc. 123 (1995), 2949-2954.
  11. C.-M. Cheng, C. K. Li, On the Hu-Hurley-Tam conjecture concerning the generalized numerical range, Linear Algebra Appl. 305 (2000), 87-97.
  12. 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.
  13. C.-M. Cheng, X-Q Jin, Some stability properties of T. Chan’s preconditioner, Linear Algebra Appl. 395 (2005), 361-365.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. C.-M. Cheng, S.-W. Vong, D. Wenzel, Commutators with maximal Frobenius norm, Linear Algebra Appl. 432 (2010), 292-306.
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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
  27. 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.
  28. 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.
  29. C.-M. Cheng, C. Lei, On Schatten p-norms of commutators, Linear Algebra Appl. 484 (2015), 409-434.
  30. C.-M. Cheng, Y. Liang, Some sharp bounds for the commutator of real matrices, Linear Algebra Appl. 521 (2017), 263-282.
  31. Z.-J. Xie, C.-M. Cheng, X. Jin, Some norm inequalities for commutators of contracted tensor products, Linear Algebra Appl. 540 (2018), 244-256.
  32. 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.
  33. 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.
  34. C.-M. Cheng, D. O. Akintoye, R. Jiao, Commutator bounds and region of singular values of the commutator with a rank one matrix, Linear Algebra Appl. 613 (2021), 347-376.
  35. C.-M. Cheng, K. L. Hoi, Sharp bounds for the operator norm of commutator, Filomat 37:27 (2023) 9183-9195.
  36. W. K. Sio, C.-M. Cheng, A note on a conjecture from distillability of quantum entanglement, Linear Algebra Appl. 707 (2025), 152-161.

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@um.edu.mo