{"id":963,"date":"2020-06-11T14:57:12","date_gmt":"2020-06-11T06:57:12","guid":{"rendered":"https:\/\/www.fst.um.edu.mo\/personal\/?page_id=963"},"modified":"2025-04-11T16:30:51","modified_gmt":"2025-04-11T08:30:51","slug":"fstcmc","status":"publish","type":"page","link":"https:\/\/www.fst.um.edu.mo\/personal\/fstcmc\/","title":{"rendered":"Che Man CHENG"},"content":{"rendered":"\t\t
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<\/td>Che Man CHENG, Raymond \u912d\u667a\u6587
Associate Professor
Associate Head of Department of Mathematics (MAT)<\/td><\/tr><\/tbody><\/table>

Academic Qualification<\/h3>
  • PhD (Mathematics), The University of Hong Kong, Hong Kong (1991)<\/li>
  • B.Sc. (Mathematics), The University of Hong Kong, Hong Kong (1987)<\/li><\/ul>

    Working Experience<\/h3>
    2016-<\/td>Associate Head of Department of Mathematics, FST, UM<\/td><\/tr>
    2000-<\/td>Associate professor, FST, UM<\/td><\/tr>
    2002-2005,<\/td>Head of Department of Mathematics, FST, UM<\/td><\/tr>
    1999-2001,<\/td>Member of the Management Committee of Faculty of Education, UM<\/td><\/tr>
    1997-2002,<\/td>Coordinator of Mathematics program, FST, UM<\/td><\/tr>
    1992-2000,<\/td>Assistant professor, FST, UM<\/td><\/tr><\/tbody><\/table>

    Teaching<\/h3>

    B.Sc. Courses<\/h4>
    1. Calculus I (MATB110)<\/li>
    2. Calculus II (MATB120)<\/li>
    3. Complex Analysis (EDUC354)<\/li>
    4. Linear Algebra (MATH103)<\/li>
    5. Operations Research (MATB226)<\/li>
    6. Quantitative Reasoning for Science and Technology (GEST1004)<\/li>
    7. Mathematical Analysis I (MATH101)<\/li>
    8. Mathematical Analysis II (MATH102)<\/li>
    9. Mathematical Analysis III (MATB350)<\/li><\/ol>

      M.Sc. Courses<\/h4>
      1. Matrix Analysis (MATH7008)<\/li><\/ol>

        Research<\/h3>

        Research Interests<\/h4>
        • Matrix theory, including numerical ranges, eigenvalues and singular values, norms of commutators, and Hurwitz matrix equations<\/li><\/ul>

          Publications<\/h3>
          1. C.-M. Cheng, A note on interlacing polynomial,\u00a0Southeast Asian Bull. Math<\/em>.\u00a014<\/strong>\u00a0(1990), 25-26.<\/li>
          2. C.-M. Cheng, Two results on\u00a0C<\/em>-congruence numerical radii,\u00a0Tamkang\u00a0J. Math<\/em>.\u00a021<\/strong>\u00a0(1990), 59-64.<\/li>
          3. C.-M. Cheng, An approximation problem with respect to symmetric gauge functions with applications to matrix spaces,\u00a0Linear and Multilinear Algebra <\/em>29<\/strong>\u00a0(1991), 169-180.<\/li>
          4. Y.-H. Au-Yeung, C. M. Cheng, Permutation matrices whose convex combinations are\u00a0orthostochastic,\u00a0Linear Algebra Appl<\/em>.\u00a0150<\/strong>\u00a0(1991), 243-253.<\/li>
          5. C.-M. Cheng, Independence of eigenvalues and independence of singular values of submatrices,\u00a0Linear Algebra Appl<\/em>.\u00a0166<\/strong>\u00a0(1992), 115-129.<\/li>
          6. C.-M. Cheng, Cases of equality for a singular value inequality of the\u00a0Hadamard\u00a0product,\u00a0Linear Algebra Appl<\/em>.\u00a0177<\/strong>\u00a0(1992), 209-231.<\/li>
          7. Y.-H. Au-Yeung, C.-M. Cheng, Two formulas for the Radon-Hurwitz number, Linear and Multilinear Algebra <\/em>34<\/strong>\u00a0(1993), 59-65.<\/li>
          8. C.-M. Cheng,\u00a0On\u00a0the decomposable numerical range of\u00a0\u03bbI-N, Linear and Multilinear Algebra <\/em>37<\/strong>\u00a0(1994), 197-205.<\/li>
          9. C.-M. Cheng, C.-K. Li, Some geometrical properties of the decomposable numerical range,\u00a0Linear and Multilinear Algebra <\/em>37<\/strong>\u00a0(1994), 207-212.<\/li>
          10. C.-M. Cheng,\u00a0On\u00a0principal sections of a pair of forms,\u00a0Proc. Amer. Math. Soc<\/em>.\u00a0123<\/strong>\u00a0(1995), 2949-2954.<\/li>
          11. C.-M. Cheng, C. K. Li, On the Hu-Hurley-Tam conjecture concerning the generalized numerical range,\u00a0Linear Algebra Appl<\/em>.\u00a0305<\/strong>\u00a0(2000), 87-97.<\/li>
          12. C.-M. Cheng, R. A. Horn, C.-K. Li, Inequalities and equalities for the Cartesian decomposition of complex matrices,\u00a0Linear Algebra Appl.<\/em>\u00a0341<\/strong> (2002), 219-237.<\/li>
          13. C.-M. Cheng, X-Q\u00a0Jin, Some stability properties of T. Chan\u2019s preconditioner,\u00a0Linear Algebra Appl. <\/em>395<\/strong>\u00a0(2005), 361-365.<\/li>
          14. C.-M. Cheng, X.-Q.\u00a0Jin, Y-M Wei, Stability properties of\u00a0superoptimal\u00a0preconditioner from numerical range,\u00a0Numer. Linear Algebra Appl.<\/em>\u00a013<\/strong>\u00a0(2006), 513-521.<\/li>
          15. Y.-H. Au-Yeung, C.-M. Cheng,\u00a0On\u00a0the pure imaginary\u00a0quaternionic\u00a0solutions of the Hurwitz matrix equations,\u00a0Linear Algebra Appl.<\/em>\u00a0419<\/strong>\u00a0(2006), 630-642.<\/li>
          16. C.-M. Cheng, X.-Q.\u00a0Jin, V.-K. Sin, Stability properties of T. Chan\u2019s preconditioner from numerical range,\u00a0Numerical Mathematics: A Journal of Chinese Universities<\/em>\u00a0(English series)\u00a016<\/strong>\u00a0(2007), 28-36.<\/li>
          17. C. M. Cheng, X.-Q.\u00a0Jin, S.-W.\u00a0Vong, W. Wang, A note on spectra of optimal and\u00a0superoptimal\u00a0preconditioned matrices,\u00a0Linear Algebra Appl.<\/em>\u00a0422<\/strong>\u00a0(2007), 482-485.<\/li>
          18. C.-M. Cheng, I.-C. Law, S.-I Leong, Eigenvalue equalities for ordinary and\u00a0Hadamard\u00a0products of powers of positive semidefinite matrices,\u00a0Linear Algebra Appl.<\/em>\u00a0422<\/strong>\u00a0(2007), 771-787.<\/li>
          19. C.-M. Cheng, K.-L.\u00a0Cheok, I.-T. Leong, 3×3 pure imaginary\u00a0quaternionic\u00a0solutions of the Hurwitz matrix equations,\u00a0Linear and Multilinear Algebra<\/em>\u00a058<\/strong>\u00a0(2010), 863-874.<\/li>
          20. C.-M. Cheng, S.-W.\u00a0Vong, D. Wenzel, Commutators with maximal\u00a0Frobenius\u00a0norm,\u00a0Linear Algebra Appl<\/em>.\u00a0432<\/strong>\u00a0(2010), 292-306.<\/li>
          21. K.-S. Fong, C.-M. Cheng, I.-K. Lok, Another unitarily invariant norm attaining the minimum norm bound for commutators,\u00a0Linear Algebra Appl<\/em>.\u00a0433<\/strong>\u00a0(2010), 1793-1797.<\/li>
          22. C.-M. Cheng, K.-S. Fong, I.-K. Lok, Another proof for commutators with maximal\u00a0Frobenius\u00a0norm,\u00a0Recent Advances in Scientific Computing and Matrix Analysis<\/em>, p. 9-14, Editors: X.-Q.\u00a0Jin, H.-W. Sun, S.-W.\u00a0Vong, International Press, 2011.<\/li>
          23. K.-S. Fong, I.-K. Lok, C.-M. Cheng, A note on the norm of commutator and the norm of XY-YX^T,\u00a0Linear Algebra Appl<\/em>.\u00a0435<\/strong>\u00a0(2011), 1191-1201.<\/li>
          24. C.-M. Cheng, K.-S. Fong, W.-F. Lei,\u00a0On\u00a0some norm inequalities involving the commutator and XY-YX^T,\u00a0Linear Algebra Appl<\/em>.\u00a0438<\/strong>\u00a0(2013), 2793-2807.<\/li>
          25. C.-M. Cheng, Y. Gao, A note on numerical range and product of matrices,\u00a0Linear Algebra Appl<\/em>.\u00a0438<\/strong>\u00a0(2013), 3139-3143. Corrigendum,\u00a0Linear Algebra Appl<\/em>.\u00a0459<\/strong>\u00a0(2014), 622-624.<\/li>
          26. C.-M. Cheng, X.-Q.\u00a0Jin, Matrix decomposition,\u00a0Encyclopedia of Social Network Analysis and Mining<\/em>, p. 880-890, Springer Science and Business Media, New York, 2014. ISBN 978-1-4614-6169-2<\/li>
          27. R.\u00a0Alizadeh, M. B.\u00a0Asadi, C.-M. Cheng, W. Hong, C.-K. Li, Spectral radius, numerical radius, and the product of operators,\u00a0J. Math. Anal. Appl<\/em>.\u00a0423<\/strong>\u00a0(2015), 639-645.<\/li>
          28. C.-M. Cheng, X.-Q.\u00a0Jin, S.-W.\u00a0Vong, A survey on the\u00a0B\u00f6ttcher-Wenzel conjecture and related problems,\u00a0Oper. Matrices<\/em>,\u00a09<\/strong>\u00a0(2015), 659-673.<\/li>
          29. C.-M. Cheng, C. Lei, On\u00a0Schatten\u00a0p-norms of commutators,\u00a0Linear Algebra Appl<\/em>.\u00a0484<\/strong>\u00a0(2015), 409-434.<\/li>
          30. C.-M. Cheng, Y. Liang, Some sharp bounds for the commutator of real matrices,\u00a0Linear Algebra Appl<\/em>.\u00a0521<\/strong>\u00a0(2017), 263-282.<\/li>
          31. Z.-J.\u00a0Xie, C.-M. Cheng, X.\u00a0Jin, Some norm inequalities for commutators of contracted tensor products,\u00a0Linear Algebra Appl<\/em>.<\/em>\u00a0540<\/strong>\u00a0(2018), 244-256.<\/li>
          32. C.-M. Cheng, Y. Liang, Singular values, eigenvalues and diagonal elements of the commutator of 2×2 rank one matrices,\u00a0Electron. J. Linear Algebra<\/em>,\u00a036<\/strong>\u00a0(2020), 1-20.<\/li>
          33. C.-M. Cheng, R. Jiao, Proof of Wenzel\u2019s conjecture concerning singular values of the commutator of rank one matrices,\u00a0Linear Algebra Appl<\/em>.\u00a0592<\/strong> (2020), 165-174.<\/li>
          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<\/em>. 613<\/strong> (2021), 347-376.<\/li>
          35. C.-M. Cheng, K. L. Hoi, Sharp bounds for the operator norm of commutator, Filomat 37:27 (2023) 9183-9195.<\/li>
          36. W. K. Sio, C.-M. Cheng, A note on a conjecture from distillability of quantum entanglement, Linear Algebra Appl<\/i>. 707<\/b> (2025), 152-161.<\/li>
          37. W. Fang, C.M. Cheng, On some conjectures concerning the B\u00f6ttcher-Wenzel inequalities for weighted Frobenius norm, Linear Algebra Appl<\/i>. 718 (2025), 1-13.<\/li><\/ol>

            Contact Details<\/h3>

            Faculty of Science and Technology
            University of Macau, E11
            Avenida da Universidade, Taipa,
            Macau, China<\/p>

            Room: E11-3065
            Telephone: (853) 8822-4457
            Fax: (853) 8822-2426
            Email: fstcmc@um.edu.mo<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

            Che Man CHENG, Raymond \u912d\u667a\u6587Associate ProfessorAssociate 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 … <\/p>\n

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