Publications of Nam-Kiu Tsing
(last updated: May, 2008)
Journal articles
- (with L.C. Chan and M.K. Ng) Spectral Analysis for HSS Preconditioners, Numerical Mathematics: Theory, Methods and Applications, 1 (2008) 57--77.
- (with C.K. Li and B.S. Tam) Linear maps preserving permutation and
stochastic matrices, Linear Algebra and Its Applications, 341 (2002) 5--22.
- (with G. Cheung) On star-centers of some generalized numerical ranges and
diagonals of normal matrices,
Linear Algebra and Its Applications, 337 (2001) 109--119.
- (with J. Lam and H.K Tso) Robust deadbeat regulation,
International Journal of Control, 67 (1997) 587--602.
- (with C.K. Li and F.Z. Zhang) Norm hull of vectors and matrices,
Linear Algebra and Its Applications, 257 (1997) 1--27.
- (with W.S. Cheung) The C-numerical range of matrices
is star-shaped, Linear and Multilinear Algebra, 41 (1996) 245--250.
- (with C.K. Li and F. Uhlig) Numerical ranges of an operator on an
infinite inner product space, Electronic Journal of Linear
Algebra, 1 (1996), 1--17.
- (with C.K. Li) Linear maps relating different unitary similarity
orbits or different generalized numerical ranges, Linear
Algebra and Its Applications, 223/224 (1995), 463--481.
- (with M.K.H. Fan and E.I. Verriest) On analyticity of functions
involving eigenvalues, Linear Algebra and its Applications,
207 (1994), 159-180.
- (with A. Tits) When is the multiaffine image of a cube a convex
polygon? Systems and Control Letters, 20 (1993),
439-445.
- (with C.K. Li) Linear operators leaving a class of matrices
with fixed singular values invariant, Linear and Multilinear
Algebra, 34 (1993), 41-49.
- (with C.K. Li) A survey on linear preserver problems,
Chapter 5: Linear preservers on functions of singular values;
Chapter 6: Linear preservers of numerical ranges, numerical radii
and USI norms;
Chapter 7: Linear preservers of relations and equivalence relations,
Linear and Multilinear Algebra, 33 (1992), 53-84.
- (with C.K. Li) Linear preserver problems: a brief introduction
and some special techniques, Linear Algebra and its
Applications, 162-164 (1992), 217-236.
- (with C.K. Li and L. Rodman) Linear operators preserving certain
equivalence relations originating in system theory, Linear
Algebra and its Applications, 161 (1992), 165-225.
- (with C.K. Li) G-invariant norms and G(c) radii,
Linear Algebra and its Applications, 150 (1991),
179-194.
- (with C.K. Li) Matrices with circular symmetry on their unitary
orbits or C-numerical ranges, Proc. Amer. Math. Soc.,
111 (1991), 19-28.
- (with C.K. Li) On the k-th matrix numerical range,
Linear and Multilinear Algebra, 28 (1991), 229-239.
- (with R.A. Horn and C.K. Li) Linear operators preserving certain
equivalence relations on matrices, SIAM Journal on Matrix
Analysis and Applications, 12 (1991), 195-204.
- (with C.K. Li) Duality between some linear preserver problems III:
c-spectral norms and (skew-)symmetric matrices with
fixed singular values, Linear Algebra and its Applications,
143 (1991), 67-97.
- (with F. Uhlig) Inertia, numerical range and zeros of quadratic
forms for matrix pencils, SIAM Journal on Matrix Analysis
and Applications, 12 (1991), 146-159.
- (with C.K. Li) Linear operators preserving unitary similarity
invariant norms, Linear and Multilinear Algebra,
27 (1990), 213-224.
- Convexity of the largest singular value of
eDA0e-D
-- a convexity lemma, IEEE Transactions on Automatic
Control, 35 (1990), 748-749.
- (with C.K. Li) Linear operators preserving certain functions
on singular values of matrices, Linear and Multilinear
Algebra, 26 (1990), 133-143.
- (with C.K. Li) Linear operators preserving unitarily invariant
norms of matrices, Linear and Multilinear Algebra,
26 (1990), 119-132.
- (with C.K. Li) Norms on Cartesian product of linear spaces,
Tamkang J. of Math., 21 (1990), no.1, 35-39.
- On the norms used in computing the structured singular value,
IEEE Transactions on Automatic Control, 35 (1990),
no.2, 201-203.
- (with C.K. Li) G-invariant hermitian forms and
G-invariant elliptical norms, SIAM Journal on Matrix
Analysis and Applications, 10 (1989) 435-445.
- (with C.K. Li and C.H. Sung) c-Convex matrices:
characterizations, inclusion relations and normality,
Linear and Multilinear Algebra, 25 (1989), 275-287.
- (with C.K. Li) Distance to the convex hull of the unitary orbit
with respect to unitary similarity invariant norms, Linear and
Multilinear Algebra, 25 (1989), 93-103.
- (with C.K. Li) The numerical range of derivations, Linear
Algebra and its Applications, 119 (1989), 97-119.
- (with C.K. Li) Norms that are invariant under unitary similarities,
and the C-numerical radii, Linear and Multilinear
Algebra, 24 (1989), 209-222.
- (with C.K. Li) Duality between some linear preserver problems
II : isometries with respect to c-spectral norms and
matrices with fixed singular values, Linear Algebra and its
Applications, 110 (1988), 181-212.
- (with C.K. Li and B.S. Tam) Linear operators preserving the
(p,q)-numerical range, Linear Algebra and its
Applications, 110 (1988), 75-89.
- (with C.K. Li) Duality between some linear preservers problems:
the invariance of C-numerical range, C-numerical
radius and certain matrix set, Linear and Multilinear
Algebra, 23 (1988), 353-362.
- (with C.K. Li) Linear operators preserving the decomposable
numerical radius, Linear and Multilinear Algebra, 23
(1988), 333-341.
- (with C.K. Li) Some isometries of rectangular complex matrices,
Linear and Multilinear Algebra, 23 (1988), 47-53.
- (with C.K. Li) Linear operators that preserve the
c-numerical range or radius of matrices, Linear and
Multilinear Algebra, 23 (1988), 27-46.
- (with Y.T. Poon) Inclusion relations between orthostochastic
matrices and products of pinching matrices, Linear and
Multilinear Algebra, 21 (1987), 253-259.
- Is aI
(1-a)J
orthostochastic?, Current Trends
in Matrix Theory, 399-403, Elsevier Science Publishing Co. Inc.
(1987).
- (with C.K. Li) On the unitarily invariant norms and some related
results, Linear and Multilinear Algebra, 20 (1987),
107-119.
- (with C.K. Li and T.Y. Tam) The generalized spectral radius,
numerical radius and spectral norm, Linear and Multilinear
Algebra, 16 (1984), 215-237.
- (with M.K. Siu) You are living in a world of mathematics,
International Journal of Mathematical Education
in Science and Technology, 15 (1984), 47-52.
- The constrained bilinear form and the C-numerical range,
Linear Algebra and its Applications, 56 (1984),
195-206.
- Infinite-dimensional Banach spaces must have uncountable
basis -- an elementary proof, Amer. Math. Monthly, 91
(1984), 505-506.
- (with Y.H. Au-Yeung) Some theorems on the generalized numerical
ranges, Linear and Multilinear Algebra, 15 (1984), 3-11.
- (with Y.H. Au-Yeung) An extension of the Hausdorff-Toeplitz
theorem on the numerical range, Proc. Amer. Math. Soc.,
89 (1983), 215-218.
- (with Y.H. Au-Yeung) A conjecture of Marcus on the generalized
numerical range, Linear and Multilinear Algebra, 14
(1983), 235-239.
- Diameter and minimal width of the numerical range, Linear and
Multilinear Algebra, 14 (1983), 179-185.
- On the shape of the generalized numerical ranges, Linear and
Multilinear Algebra, 10 (1981), 173-182.
Conference papers and proceedings
- (with W.K. Ching, K. Cheng, L. Li, and A.S.T. Wong) Weighted Local Least Squares Imputation Method for Missing Value Estimation, The International Symposium on Optimization and Systems Biology (OSB 2007), Lecture Notes in Operations Research 7, (2007) 280--287.
- (with J. Lam and H.K. Tso) On the design of robust deadbeat regulators,
Proceedings of 35th IEEE Conference on Decision and Control,
Kobe, Japan, December 11-31, 1996.
- (with A. Tits) On the multiaffine image of a cube,
Robustness of Dynamic Systems with Parameter Uncertainties,
105-110, Berkh\"{a}user Verlag, 1992.
- (with J. Barlow, M. Fan, M. Takahashi, M. Tischler, and
A. Tits) On the design of decoupling controllers for advanced
rotorcraft in the hover case, American Institute of
Aeronautics and Astronautics 29th Aerospace Sciences Meeting,
Reno, Nevada, January, 1991.
PhD dissertations
- Computer-Based Techniques for Control System Design,
with Applications to Rotorcraft Control, Electrical Engineering
Department, University of Maryland, 1992.
- A Study of Generalized Numerical Ranges, Department of
Mathematics, The University of Hong Kong, 1983.
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