Cheng Che Man, Raymond  鄭智文 Associate Professor

• PhD (Mathematics), The University of Hong Kong, Hong Kong (1991)
• B.Sc. (Mathematics), The University of Hong Kong, Hong Kong (1987)

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

B.Sc. Courses

1. Mathematical Analysis I (MATH101)
2. Mathematical Analysis II (MATH102)
3. Linear Algebra (MATH103)
4. Operations Research I (SFTW122)
5. Algebra I (EDUC202)
6. Algebra II (EDUC203)
7. Operational Research (EDUC413)

1. Algebra (IMMT110)
2. Matrix Analysis (IMMT125)
3. Matrix Analysis (IMAT008)

Research Interests

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

1. A note on interlacing polynomial, Southeast Asian Bull. Math. 14 (1990), 25-26.
2. Two results on C-congruence numerical radii, Tamkang J. Math. 21 (1990), 59-64.
3. An approximation problem with respect to symmetric gauge functions with applications to matrix spaces, Linear and Multilinear Algebra29 (1991), 169-180.
4. (with Y.H. Au-Yeung) Permutation matrices whose convex combinations are orthostochastic, Linear Algebra Appl. 150 (1991), 243-253.
5. Independence of eigenvalues and independence of singular values of submatrices, Linear Algebra Appl. 166 (1992), 115-129.
6. Cases of equality for a singular value inequality of the Hadamard product, Linear Algebra Appl. 177 (1992), 209-231.
7. (with Y.H. Au-Yeung) Two formulas for the Radon-Hurwitz number, Linear and Multilinear Algebra34 (1993), 59-65.
8. On the decomposable numerical range of , Linear and Multilinear Algebra37 (1994), 197-205.
9. (with C.K. Li) Some geometrical properties of the decomposable numerical range, Linear and Multilinear Algebra37 (1994), 207-212.
10. On principal sections of a pair of forms, Proc. Amer. Math. Soc. 123 (1995), 2949-2954.
11. (with C. K. Li) On the Hu-Hurley-Tam conjecture concerning the generalized numerical range, Linear Algebra Appl. 305 (2000), 87-97.
12. (with R. A. Horn and C. K. Li) Inequalities and equalities for the Cartesian decomposition of complex matrices, Linear Algebra Appl. 341 (2002), 219-237.
13. (with X-Q Jin) Some stability properties of T. Chan’s preconditioner, Linear Algebra Appl.395 (2005), 361-365.
14. (with X.-Q. Jin and Y-M Wei) Stability properties of superoptimal preconditioner from numerical range, Numer. Linear Algebra Appl. 13 (2006), 513-521.
15. (with Y.-H. Au-Yeung) On the pure imaginary quaternionic solutions of the Hurwitz matrix equations, Linear Algebra Appl. 419 (2006), 630-642.
16. (with X.-Q. Jin and 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. (with X.-Q. Jin, S.-W. Vong and W. Wang) A note on spectra of optimal and superoptimal preconditioned matrices, Linear Algebra Appl. 422 (2007), 482-485.
18. (with I.-C. Law and S.-I Leong) Eigenvalue equalities for ordinary and Hadamard products of powers of positive semidefinite matrices, Linear Algebra Appl. 422 (2007), 771-787.
19. (with S.-W. Vong and D. Wenzel) Commutators with maximal Frobenius norm, (to appear in Linear Algebra Appl.)
20. (with K.-L. Cheok and I.-T. Leong) 3x3 pure imaginary quaternionic solutions of the Hurwitz matrix equations, (to appear in Linear Multilinear Algebra)

Faculty of Science and Technology
University of Macau
Av. Padre Tomás Pereira, Taipa,
Macau, China

Room: N407
Telephone: (853) 8397-4457
Fax: (853) 28838314
Email: fstcmc