## Li, Chi-Kwong

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 Author ID: li.chi-kwong Published as: Li, Chi-Kwong; Li, C. K.; Li, C.-K.; Li, Chen Kuan; Li, Chi-kwong; Li, Chi Kwong more...less Homepage: http://people.wm.edu/~cklixx/ External Links: MGP · dblp
 Documents Indexed: 340 Publications since 1984 9 Contributions as Editor Co-Authors: 185 Co-Authors with 316 Joint Publications 4,251 Co-Co-Authors
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### Co-Authors

 30 single-authored 59 Poon, Yiu-Tung 48 Sze, Nung-Sing 31 Tsing, Nam-Kiu 28 Rodman, Leiba X. 15 Mathias, Roy 13 Poon, Edward 9 Cheung, Waishun 8 Huang, Zejun 8 Šemrl, Peter 7 Choi, Man-Duen 7 Cui, Jianlian 7 Pelejo, Diane Christine P. 6 Bebiano, Natália Isabel Quadros 6 Kuzma, Bojan 6 Pierce, Stephen J. 5 Chan, Jorting 5 da Providência Santarém e Costa, João 5 Horn, Roger Alan 5 Hou, Jinchuan 5 Schneider, Hans 5 Wang, Kuo-Zhong 4 Cheng, Cheman 4 Chiang, Hanley 4 Clark, Sean 4 Fošner, Ajda 4 Gau, Hwa-Long 4 Ilišević, Dijana 4 Johnson, Charles Royal 4 Lau, Pan-Shun 4 Merino, Dennis I. 4 Milligan, Thomas 4 Nakahara, Mikio 4 Tam, Bit-Shun 4 Tam, Tin-Yau 4 Tsai, Ming Cheng 4 Wang, Xuefeng 4 Zaharia, Alexandru 3 Ando, Tsuyoshi 3 Kirkland, Stephen J. 3 Lešnjak, Gorazd 3 Mehta, Paras P. 3 Petek, Tatjana 3 Schreiber, Sebastian J. 3 So, Wasin 3 Spitkovsky, Ilya Matvey 3 Wang, Ya-Shu 3 Woerdeman, Hugo Jan 3 Zhang, Fuzhen 2 Bai, Zhongzhi 2 Binding, Paul Anthony 2 Bolotnikov, Vladimir 2 Chang, Stanley S. 2 Chien, Mao-Ting 2 Đoković, Dragomir Ž. 2 Fallat, Shaun M. 2 Fonseca, Carlos M. 2 Forstall, Virginia 2 Friedland, Shmuel 2 Fung, Chi-Hang Fred 2 Furtado, Susana 2 Golub, Gene Howard 2 Guralnick, Robert Michael 2 Hambric, Christopher Logan 2 Herman, Aaron 2 Kovačec, Alexander 2 Li, Rencang 2 Nakazato, Hiroshi 2 Paulsen, Vern Ival 2 Qi, Xiaofei 2 Rastogi, Ashwin 2 Shi, Junping 2 Sourour, Ahmed Ramzi 2 Stanford, David P. 2 Strang, William Gilbert 2 Tomita, Hiroyuki 2 van den Driessche, Pauline 2 Wong, Wing-Keung 2 Wu, Peiyuan 2 Yannello, Vincent 2 Zeng, Bei 1 Albert, Chase 1 Alizadeh, Rahim 1 Alwill, Michael 1 Asadi, Mohammad B. 1 Au-Yeung, Yik-Hoi 1 Beasley, LeRoy B. 1 Bhatia, Rajendra 1 Botelho-Andrade, Sara 1 Brualdi, Richard Anthony 1 Cao, Ningping 1 Chan, Jien-Tsai 1 Chen, Jianxin 1 Chu, Sidney C. K. 1 Coleman, Todd P. 1 Crowder, Tanner 1 Curtis, Frank E. 1 Davis, Chandler 1 Ding, Wenxuan 1 Dobovišek, Mirko 1 Drew, John H. ...and 90 more Co-Authors
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### Serials

 89 Linear Algebra and its Applications 82 Linear and Multilinear Algebra 19 SIAM Journal on Matrix Analysis and Applications 17 ELA. The Electronic Journal of Linear Algebra 13 Proceedings of the American Mathematical Society 12 Journal of Mathematical Analysis and Applications 7 Canadian Mathematical Bulletin 7 Operators and Matrices 6 Canadian Journal of Mathematics 5 Bulletin of the Australian Mathematical Society 5 Rocky Mountain Journal of Mathematics 4 Journal of Mathematical Physics 4 Studia Mathematica 4 Acta Scientiarum Mathematicarum 4 Journal of Operator Theory 4 Journal of Physics A: Mathematical and Theoretical 3 American Mathematical Monthly 3 Journal of Functional Analysis 3 Mathematical Inequalities & Applications 3 Journal of the Australian Mathematical Society 2 International Journal of Mathematical Education in Science and Technology 2 Mathematics of Computation 2 SIAM Review 2 Taiwanese Journal of Mathematics 2 Quantum Information Processing 2 International Journal of Quantum Information 1 Communications in Mathematical Physics 1 Discrete Mathematics 1 Journal of Mathematical Biology 1 Physics Letters. A 1 Bulletin of Mathematical Biology 1 Mathematics Magazine 1 American Journal of Mathematics 1 Archiv der Mathematik 1 BIT 1 Bulletin of the London Mathematical Society 1 Glasgow Mathematical Journal 1 Integral Equations and Operator Theory 1 Journal of Combinatorial Theory. Series A 1 Numerische Mathematik 1 Tamkang Journal of Mathematics 1 Transactions of the American Mathematical Society 1 SIAM Journal on Discrete Mathematics 1 Economics Letters 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Scientific Computing 1 Bulletin of the Institute of Combinatorics and its Applications 1 Integral Transforms and Special Functions 1 Positivity 1 Novi Sad Journal of Mathematics 1 Journal of Inequalities and Applications 1 The Asian Journal of Mathematics 1 New Journal of Physics 1 RAIRO. Operations Research 1 Communications in Mathematical Sciences 1 Journal of Biological Dynamics 1 Banach Journal of Mathematical Analysis 1 Discrete and Continuous Dynamical Systems. Series S 1 Quantum Information & Computation 1 Textos de Matemática 1 Advances in Operator Theory
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### Fields

 275 Linear and multilinear algebra; matrix theory (15-XX) 88 Operator theory (47-XX) 32 Quantum theory (81-XX) 26 Functional analysis (46-XX) 19 Numerical analysis (65-XX) 17 Combinatorics (05-XX) 12 Group theory and generalizations (20-XX) 10 Information and communication theory, circuits (94-XX) 6 General and overarching topics; collections (00-XX) 6 Convex and discrete geometry (52-XX) 5 Biology and other natural sciences (92-XX) 4 History and biography (01-XX) 4 Geometry (51-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Nonassociative rings and algebras (17-XX) 2 Real functions (26-XX) 2 Difference and functional equations (39-XX) 2 Probability theory and stochastic processes (60-XX) 2 Operations research, mathematical programming (90-XX) 1 Mathematical logic and foundations (03-XX) 1 Associative rings and algebras (16-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Systems theory; control (93-XX)

### Citations contained in zbMATH Open

278 Publications have been cited 3,187 times in 1,881 Documents Cited by Year
Linear preserver problems: A brief introduction and some special techniques. Zbl 0762.15016
Li, Chi-Kwong; Tsing, Nam-Kiu
1992
Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices. Zbl 1114.65034
Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong
2007
Linear preserver problems. Zbl 0991.15001
Li, Chi-Kwong; Pierce, Stephen
2001
Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices. Zbl 1116.65039
Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong
2006
Geometric means. Zbl 1063.47013
Ando, T.; Li, Chi-Kwong; Mathias, Roy
2004
Some general techniques on linear preserver problems. Zbl 0964.15004
Guterman, Alexander; Li, Chi-Kwong; Šemrl, Peter
2000
Applications of Perron-Frobenius theory to population dynamics. Zbl 1015.91059
Li, Chi-Kwong; Schneider, Hans
2002
$$C$$-numerical ranges and $$C$$-numerical radii. Zbl 0814.15022
Li, Chi-Kwong
1994
Numerical range of matrix polynomials. Zbl 0814.15023
Li, Chi-Kwong; Rodman, Leiba
1994
Canonical forms, higher rank numerical ranges, totally isotropic subspaces, and matrix equations. Zbl 1152.15027
Li, Chi-Kwong; Sze, Nung-Sing
2008
Maps preserving product $$XY -YX^*$$ on factor von Neumann algebras. Zbl 1183.47031
Cui, Jianlian; Li, Chi-Kwong
2009
Mappings preserving spectra of products of matrices. Zbl 1113.15002
Chan, Jor-Ting; Li, Chi-Kwong; Sze, Nung-Sing
2007
A note on extreme correlation matrices. Zbl 0804.15011
Li, Chi-Kwong; Tam, Bit-Shun
1994
On the evolution of dispersal in patchy landscapes. Zbl 1100.39011
Kirkland, Stephen; Li, Chi-Kwong; Schreiber, Sebastian J.
2006
Convexity of the joint numerical range. Zbl 0945.15019
Li, Chi-Kwong; Poon, Yiu-Tung
2000
A simple proof of the elliptical range theorem. Zbl 0857.15020
Li, Chi-Kwong
1996
Mappings on matrices: invariance of functional values of matrix products. Zbl 1110.15005
Chan, Jor-Ting; Li, Chi-Kwong; Sze, Nung-Sing
2006
Maps preserving the nilpotency of products of operators. Zbl 1124.47026
Li, Chi-Kwong; Šemrl, Peter; Sze, Nung-Sing
2007
Jordan isomorphisms and maps preserving spectra of certain operator products. Zbl 1134.47028
Hou, Jinchuan; Li, Chi-Kwong; Wong, Ngai-Ching
2008
$$G$$-invariant norms and bicircular projections. Zbl 1110.15025
Fošner, Maja; Ilišević, Dijana; Li, Chi-Kwong
2007
Maps preserving the spectrum of generalized Jordan product of operators. Zbl 1185.47036
Hou, Jinchuan; Li, Chi-Kwong; Wong, Ngai-Ching
2010
Condition for the higher rank numerical range to be non-empty. Zbl 1172.15014
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2009
A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027
Li, Chi-Kwong; Li, Ren-Cang
2005
G-invariant norms and G(c)-radii. Zbl 0722.15027
Li, Chi-Kwong; Tsing, Nam-Kiu
1991
Determinantal and eigenvalue inequalities for matrices with numerical ranges in a sector. Zbl 1307.15029
Li, Chi-Kwong; Sze, Nung-Sing
2014
Linear operators that preserve the c-numerical range or radius of matrices. Zbl 0642.15006
Li, Chi-Kwong; Tsing, Nam-Kiu
1988
The numerical range of a nonnegative matrix. Zbl 1003.15027
Li, Chi-Kwong; Tam, Bit-Shun; Wu, Pei Yuan
2002
c-convex matrices: Characterizations, inclusion relations and normality. Zbl 0686.15010
Li, Chi-Kwong; Sung, Chen-Han; Tsing, Nam-Kiu
1989
Linear-operators preserving unitarily invariant norms of matrices. Zbl 0691.15006
Li, Chi-Kwong; Tsing, Nam-Kiu
1990
Mappings that preserve pairs of operators with zero triple Jordan product. Zbl 1130.15002
Dobovišek, M.; Kuzma, B.; Lešnjak, G.; Li, C. K.; Petek, T.
2007
Eigenvalues, singular values, and Littlewood-Richardson coefficients. Zbl 1072.15010
Fomin, Sergey; Fulton, William; Li, Chi-Kwong; Poon, Yiu-Tung
2005
Joint ranges of Hermitian matrices and simultaneous diagonalization. Zbl 0724.15020
Binding, Paul; Li, Chi-Kwong
1991
Matrices with some extremal properties. Zbl 0659.15018
Li, Chi-Kwong
1988
Generalized numerical ranges and quantum error correction. Zbl 1261.47012
Li, Chi-Kwong; Poon, Yiu-Tung
2011
Duality between some linear preserver problems. II: Isometries with respect to c-spectral norms and matrices with fixed singular values. Zbl 0655.15026
Li, Chi-Kwong; Tsing, Nam-Kiu
1988
Some aspects of the theory of norms. Zbl 0814.15021
Li, Chi-Kwong
1994
Duality between some linear preservers problems: The invariance of the C- numerical range, the C-numerical radius and certain matrix sets. Zbl 0668.15014
Li, Chi-Kwong; Tsing, Nam-Kiu
1988
A generalized numerical range: The range of a constrained sesquilinear form. Zbl 0819.15018
Li, Chi-Kwong; Mehta, Paras P.; Rodman, Leiba
1994
$$C^*$$-isomorphisms, Jordan isomorphisms, and numerical range preserving maps. Zbl 1123.47032
Gau, Hwa-Long; Li, Chi-Kwong
2007
Extremal characterizations of the Schur complement and resulting inequalities. Zbl 0948.15017
Li, Chi-Kwong; Mathias, Roy
1998
Linear operators preserving directional majorization. Zbl 0999.15030
Li, Chi-Kwong; Poon, Edward
2001
Linear transformations between matrix spaces that map one rank specific set into another. Zbl 1022.15001
Li, Chi-Kwong; Rodman, Leiba; Šemrl, Peter
2002
Maps preserving peripheral spectrum of Jordan products of operators. Zbl 1258.47054
Cui, Jianlian; Li, Chi-Kwong
2012
Unitarily invariant metrics on the Grassmann space. Zbl 1099.15024
Qiu, Li; Zhang, Yanxia; Li, Chi-Kwong
2005
The c-spectral, c-radial and c-convex matrices. Zbl 0612.15016
Li, Chi-Kwong
1987
Linear operators preserving the higher numerical radius of matrices. Zbl 0622.15017
Li, Chi-Kwong
1987
The C-convex matrices. Zbl 0635.15025
Li, Chi-Kwong
1987
Orthogonality of matrices. Zbl 1003.15028
Li, Chi-Kwong; Schneider, Hans
2002
The Lidskii-Mirsky-Wielandt theorem – additive and multiplicative versions. Zbl 0922.15010
Li, Chi-Kwong; Mathias, Roy
1999
Davis–Wielandt shells of operators. Zbl 1176.47010
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2008
Pseudospectra of special operators and pseudospectrum preservers. Zbl 1357.47007
Cui, Jianlian; Li, Chi-Kwong; Poon, Yiu-Tung
2014
Miscellaneous preserver problems. Zbl 0767.15006
Beasley, LeRoy B.; Li, Chi-Kwong; Pierce, Stephen
1992
Linear maps on selfadjoint operators preserving invertibility, positive definiteness, numerical range. Zbl 1056.47018
Li, Chi-Kwong; Rodman, Leiba; Šemrl, Peter
2003
Linear operators preserving certain equivalence relations on matrices. Zbl 0724.15007
Horn, Roger A.; Li, Chi-Kwong; Tsing, Nam-Kiu
1991
Constrained unitary dilations and numerical ranges. Zbl 0996.47003
Choi, Man-Duen; Li, Chi-Kwong
2001
Remarks on numerical ranges of operators in spaces with an indefinite metric. Zbl 0897.15012
Li, Chi-Kwong; Rodman, Leiba
1998
Some results on the $$q$$-numerical range. Zbl 0899.15017
Li, Chi-Kwong; Nakazato, Hiroshi
1998
Properties and preservers of the pseudospectrum. Zbl 1245.15028
Cui, Jianlian; Forstall, Virginia; Li, Chi-Kwong; Yannello, Vincent
2012
Higher rank numerical ranges and low rank perturbations of quantum channels. Zbl 1151.47008
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2008
Preservers for norms of Lie product. Zbl 1181.15031
Li, Chi-Kwong; Poon, Edward; Sze, Nung-Sing
2009
Matrices with circular symmetry on their unitary orbits and C-numerical ranges. Zbl 0719.15017
Li, Chi-Kwong; Tsing, Nam-Kiu
1991
Interpolation by completely positive maps. Zbl 1236.15004
Li, Chi-Kwong; Poon, Yiu-Tung
2011
Linear preservers and quantum information science. Zbl 1290.15017
Fošner, Ajda; Huang, Zejun; Li, Chi-Kwong; Sze, Nung-Sing
2013
Shapes and computer generation of numerical ranges of Krein space operators. Zbl 0905.47027
Li, Chi-Kwong; Rodman, Leiba
1998
The automorphism group of separable states in quantum information theory. Zbl 1316.81014
Friedland, Shmuel; Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2011
Polynomial numerical hulls of matrices. Zbl 1130.15017
Davis, Chandler; Li, Chi-Kwong; Salemi, Abbas
2008
The joint essential numerical range of operators: convexity and related results. Zbl 1178.47001
Li, Chi-Kwong; Poon, Yiu-Tung
2009
Duality between some linear preserver problems. III: c-spectral norms and (skew)-symmetric matrices with fixed singular values. Zbl 0712.15028
Li, Chi-Kwong; Tsing, Nam-Kiu
1991
Norms that are invariant under unitary similarities and the C-numerical radii. Zbl 0712.15029
Li, Chi-Kwong; Tsing, Nam-Kiu
1989
On the kth matrix numerical range. Zbl 0717.15018
Li, Chi-Kwong; Tsing, Nam-Kiu
1991
Graphs associated with matrices over finite fields and their endomorphisms. Zbl 1288.05158
Huang, Li-Ping; Huang, Zejun; Li, Chi-Kwong; Sze, Nung-Sing
2014
Induced operators on symmetry classes of tensors. Zbl 0984.15025
Li, Chi-Kwong; Zaharia, Alexandru
2002
Linear transformations on $$M_ n({\mathbb{R}})$$ that preserve the Ky Fan k- norm and a remarkable special case when $$(n,k)=(4,2)$$. Zbl 0658.15029
Johnson, Charles R.; Laffey, Thomas; Li, Chi-Kwong
1988
Stationary probability vectors of higher-order Markov chains. Zbl 1391.60176
Li, Chi-Kwong; Zhang, Shixiao
2015
Higher rank numerical ranges of normal matrices. Zbl 1223.15032
Gau, Hwa-Long; Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2011
Multiplicative preservers on semigroups of matrices. Zbl 1025.15001
Cheung, Wai-Shun; Fallat, Shaun; Li, Chi-Kwong
2002
Invertible preservers and algebraic groups. III: Preservers of unitary similarity (congruence) invariants and overgroups of some unitary subgroups. Zbl 0889.20027
Guralnick, Robert M.; Li, Chi-Kwong
1997
Linear operators preserving similarity classes and related results. Zbl 0809.15014
Li, Chi-Kwong; Pierce, Stephen
1994
Linear maps preserving permutation and stochastic matrices. Zbl 0998.15004
Li, Chi-Kwong; Tam, Bit-Shun; Tsing, Nam-Kiu
2002
The decomposable numerical radius and numerical radius of a compound matrix. Zbl 0588.15011
Li, Chi-Kwong
1986
On the unitarily invariant norms and some related results. Zbl 0612.15017
Li, Chi-Kwong; Tsing, Nam-Kiu
1987
Overgroups of some classical linear groups with applications to linear preserver problems. Zbl 0793.15018
Đoković, Dragomir Ž.; Li, Chi-Kwong
1994
Numerical ranges and dilations. Zbl 0952.47005
Choi, Man-Duen; Li, Chi-Kwong
2000
A class of unitarily invariant norms on $$B(H)$$. Zbl 0963.47013
Chan, Jor-Ting; Li, Chi-Kwong; Tu, Charlies C. N.
2001
Higher-rank numerical ranges and dilations. Zbl 1212.15022
Gau, Hwa-Long; Li, Chi-Kwong; Wu, Pei Yuan
2010
A note on convex stochastic dominance. Zbl 0917.90019
Wong, Wing-Keung; Li, Chi-Kwong
1999
The ultimate estimate of the upper norm bound for the summation of operators. Zbl 1116.47011
Choi, Man-Duen; Li, Chi-Kwong
2006
Linear operators preserving unitary similarity invariant norms. Zbl 0706.15028
Li, Chi-Kwong; Tsing, Nam-Kiu
1990
Isometries for unitarily invariant norms. Zbl 1073.15022
Chan, Jor-Ting; Li, Chi-Kwong; Sze, Nung-Sing
2005
A survey on linear preservers of numerical ranges and radii. Zbl 0986.15021
Li, Chi-Kwong
2001
Preservers of unitary similarity functions on Lie products of matrices. Zbl 1334.15055
Cui, Jianlian; Li, Chi-Kwong; Poon, Yiu-Tung
2016
Isometries for the vector $$(p,q)$$ norm and the induced $$(p,q)$$ norm. Zbl 0830.15023
Klaus, Anne-Louise; Li, Chi-Kwong
1995
Product of operators and numerical range preserving maps. Zbl 1098.47007
Li, Chi-Kwong; Sze, Nung-Sing
2006
Certain isometries on $$\mathbb{R}{}^ n$$. Zbl 0743.15013
Chang, Stanley S.; Li, Chi-Kwong
1992
Some convexity theorems for the generalized numerical ranges. Zbl 0869.15017
Li, Chi-Kwong
1996
Linear preservers of tensor product of unitary orbits, and product numerical range. Zbl 1281.15030
Li, Chi-Kwong; Poonl, Yiu-Tung; Sze, Nung-Sing
2013
Li, Chi-Kwong; Šemrl, Peter
2002
Linear maps preserving Ky Fan norms and Schatten norms of tensor products of matrices. Zbl 1273.15030
Fošner, Ajda; Huang, Zejun; Li, Chi-Kwong; Sze, Nung-Sing
2013
Equality of higher numerical ranges of matrices and a conjecture of Kippenhahn on Hermitian pencils. Zbl 0929.15024
Li, Chi-Kwong; Spitkowsky, Ilya; Shukla, Sudheer
1998
Generalizations of Ky Fan’s dominance theorem. Zbl 0911.15010
Li, Chi-Kwong; Mathias, Roy
1998
Higher rank matricial ranges and hybrid quantum error correction. Zbl 07333196
Cao, Ningping; Kribs, David W.; Li, Chi-Kwong; Nelson, Mike I.; Poon, Yiu-Tung; Zeng, Bei
2021
Complexifications of real Banach spaces and their isometries. Zbl 1456.46012
Ilišević, Dijana; Kuzma, Bojan; Li, Chi-Kwong; Poon, Edward
2020
Eigenvalue continuity and Geršgorin’s theorem. Zbl 1436.15008
Li, Chi-Kwong; Zhang, Fuzhen
2019
Minimum number of non-zero-entries in a $$7 \times 7$$ stable matrix. Zbl 1434.15018
Hambric, Christopher Logan; Li, Chi-Kwong; Pelejo, Diane Christine; Shi, Junping
2019
Submultiplicativity of the numerical radius of commuting matrices of order two. Zbl 1425.15020
Li, Chi-Kwong; Poon, Yiu-Tung
2019
The generalized numerical range of a set of matrices. Zbl 1405.15029
Lau, Pan-Shun; Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2019
Preservation of the joint essential matricial range. Zbl 07142409
Li, Chi-kwong; Paulsen, Vern I.; Poon, Yiu-tung
2019
Generalized numerical ranges, dilation, and quantum error correction. Zbl 1435.47011
2019
Convexity and star-shapedness of matricial range. Zbl 06933546
Lau, Pan-Shun; Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2018
The modified trace distance of coherence is constant on most pure states. Zbl 1407.81044
Johnston, Nathaniel; Li, Chi-Kwong; Plosker, Sarah
2018
Ranks of quantum states with prescribed reduced states. Zbl 1401.81027
Li, Chi-Kwong; Poon, Yiu-Tung; Wang, Xuefeng
2018
Preservers of isometries. Zbl 1413.47062
Ilišević, Dijana; Kuzma, Bojan; Li, Chi-Kwong; Poon, Edward
2018
Unitary similarity invariant function preservers of skew products of operators. Zbl 1486.47069
Cui, Jianlian; Li, Chi-Kwong; Sze, Nung-Sing
2017
Products of positive semi-definite matrices. Zbl 1400.15014
Cui, Jianlian; Li, Chi-Kwong; Sze, Nung-Sing
2017
Numerical ranges of the product of operators. Zbl 06723306
Du, Hongke; Li, Chi-Kwong; Wang, Kuo-Zhong; Wang, Yueqing; Zuo, Ning
2017
Preservers of unitary similarity functions on Lie products of matrices. Zbl 1334.15055
Cui, Jianlian; Li, Chi-Kwong; Poon, Yiu-Tung
2016
Product of operators and numerical range. Zbl 1337.47005
Chien, Mao-Ting; Gau, Hwa-Long; Li, Chi-Kwong; Tsai, Ming-Cheng; Wang, Kuo-Zhong
2016
Minkowski product of convex sets and product numerical range. Zbl 1358.52004
Li, Chi-Kwong; Pelejo, Diane Christine; Poon, Yiu-Tung; Wang, Kuo-Zhong
2016
Stationary probability vectors of higher-order Markov chains. Zbl 1391.60176
Li, Chi-Kwong; Zhang, Shixiao
2015
A new criterion and a special class of $$k$$-positive maps. Zbl 1308.15024
Hou, Jinchuan; Li, Chi-Kwong; Poon, Yiu-Tung; Qi, Xiaofei; Sze, Nung-Sing
2015
Numerical range of Lie product of operators. Zbl 1334.47006
Hou, Jinchuan; Li, Chi-Kwong; Qi, Xiaofei
2015
The spectrum of the product of operators, and the product of their numerical ranges. Zbl 1339.47004
Li, Chi-Kwong; Tsai, Ming-Cheng; Wang, Kuo-Zhong; Wong, Ngai-Ching
2015
Positivity of partitioned Hermitian matrices with unitarily invariant norms. Zbl 1325.15019
Li, Chi-Kwong; Zhang, Fuzhen
2015
Projection methods for quantum channel construction. Zbl 1327.81083
Drusvyatskiy, Dmitriy; Li, Chi-Kwong; Pelejo, Diane Christine; Voronin, Yuen-Lam; Wolkowicz, Henry
2015
Discontinuity of maximum entropy inference and quantum phase transitions. Zbl 1454.81036
Chen, Jianxin; Ji, Zhengfeng; Li, Chi-Kwong; Poon, Yiu-Tung; Shen, Yi; Yu, Nengkun; Zeng, Bei; Zhou, Duanlu
2015
Determinantal and eigenvalue inequalities for matrices with numerical ranges in a sector. Zbl 1307.15029
Li, Chi-Kwong; Sze, Nung-Sing
2014
Pseudospectra of special operators and pseudospectrum preservers. Zbl 1357.47007
Cui, Jianlian; Li, Chi-Kwong; Poon, Yiu-Tung
2014
Graphs associated with matrices over finite fields and their endomorphisms. Zbl 1288.05158
Huang, Li-Ping; Huang, Zejun; Li, Chi-Kwong; Sze, Nung-Sing
2014
Linear maps preserving the higher numerical ranges of tensor products of matrices. Zbl 1319.15005
Fošner, Ajda; Huang, Zejun; Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2014
Ranks and eigenvalues of states with prescribed reduced states. Zbl 1326.15016
Li, Chi-Kwong; Poon, Yiu-Tung; Wang, Xuefeng
2014
A review on operator quantum error correction – dedicated to Professor Mikio Nakahara on the occasion of his 60th birthday. Zbl 1299.81017
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2014
Recursive construction of noiseless subsystem for qudits. Zbl 1299.81010
Güngördü, Utkan; Li, Chi-Kwong; Nakahara, Mikio; Poon, Yiu-Tung; Sze, Nung-Sing
2014
Conditions for degradability of tripartite quantum states. Zbl 1286.81032
Fung, Chi-Hang Fred; Li, Chi-Kwong; Sze, Nung-Sing; Chau, H. F.
2014
Decomposition of quantum gates. Zbl 1288.81027
Li, Chi Kwong; Pelejo, Diane Christine
2014
Linear preservers and quantum information science. Zbl 1290.15017
Fošner, Ajda; Huang, Zejun; Li, Chi-Kwong; Sze, Nung-Sing
2013
Linear preservers of tensor product of unitary orbits, and product numerical range. Zbl 1281.15030
Li, Chi-Kwong; Poonl, Yiu-Tung; Sze, Nung-Sing
2013
Linear maps preserving Ky Fan norms and Schatten norms of tensor products of matrices. Zbl 1273.15030
Fošner, Ajda; Huang, Zejun; Li, Chi-Kwong; Sze, Nung-Sing
2013
Elementary proofs for some results on the circular symmetry of the numerical range. Zbl 1350.15012
Cheung, Wai-Shun; Li, Chi-Kwong
2013
A geometric characterization of invertible quantum measurement maps. Zbl 1283.47024
He, Kan; Hou, Jin-Chuan; Li, Chi-Kwong
2013
Linear maps preserving numerical radius of tensor products of matrices. Zbl 1309.15044
Fošner, Ajda; Huang, Zejun; Li, Chi-Kwong; Sze, Nung-Sing
2013
Decomposition of unitary matrices and quantum gates. Zbl 1267.81116
Li, Chi-Kwong; Roberts, Rebecca; Yin, Xiaoyan
2013
Maps preserving peripheral spectrum of Jordan products of operators. Zbl 1258.47054
Cui, Jianlian; Li, Chi-Kwong
2012
Properties and preservers of the pseudospectrum. Zbl 1245.15028
Cui, Jianlian; Forstall, Virginia; Li, Chi-Kwong; Yannello, Vincent
2012
Physical transformations between quantum states. Zbl 1278.81020
Huang, Zejun; Li, Chi-Kwong; Poon, Edward; Sze, Nung-Sing
2012
Every invertible matrix is diagonally equivalent to a matrix with distinct eigenvalues. Zbl 1244.15006
Choi, Man-Duen; Huang, Zejun; Li, Chi-Kwong; Sze, Nung-Sing
2012
Preservers of matrix pairs with a fixed inner product value. Zbl 1255.15033
Li, Chi-Kwong; Plevnik, Lucijan; Šemrl, Peter
2012
Generalized interlacing inequalities. Zbl 1253.15014
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2012
Maps preserving the joint numerical radius distance of operators. Zbl 1275.47013
Li, Chi-Kwong; Poon, Edward
2012
Induced metric and matrix inequalities on unitary matrices. Zbl 1239.81032
Chau, H. F.; Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2012
Generalized numerical ranges and quantum error correction. Zbl 1261.47012
Li, Chi-Kwong; Poon, Yiu-Tung
2011
Interpolation by completely positive maps. Zbl 1236.15004
Li, Chi-Kwong; Poon, Yiu-Tung
2011
The automorphism group of separable states in quantum information theory. Zbl 1316.81014
Friedland, Shmuel; Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2011
Higher rank numerical ranges of normal matrices. Zbl 1223.15032
Gau, Hwa-Long; Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2011
Efficient quantum error correction for fully correlated noise. Zbl 1252.81044
Li, Chi-Kwong; Nakahara, Mikio; Poon, Yiu-Tung; Sze, Nung-Sing; Tomita, Hiroyuki
2011
Elliptical range theorems for generalized numerical ranges of quadratic operators. Zbl 1231.47003
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2011
Norm preservers of Jordan products. Zbl 1254.15030
Kuzma, Bojan; Lesnjak, Gorazd; Li, Chi-Kwong; Petek, Tatjana; Rodman, Leiba
2011
Permutations as product of parallel transpositions. Zbl 1237.05002
Albert, Chase; Li, Chi-Kwong; Strang, Gilbert; Yu, Gexin
2011
Least-squares approximation by elements from matrix orbits achieved by gradient flows on compact Lie groups. Zbl 1228.65059
Li, Chi-Kwong; Poon, Yiu-Tung; Schulte-Herbrüggen, Thomas
2011
Evolution of unconditional dispersal in periodic environments. Zbl 1403.92189
Schreiber, Sebastian J.; Li, Chi-Kwong
2011
Tracial numerical ranges and linear dependence of operators. Zbl 1226.47007
Kuzma, Bojan; Li, Chi-Kwong; Rodman, Leiba
2011
A note on the realignment criterion. Zbl 1225.81014
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2011
Maps preserving the spectrum of generalized Jordan product of operators. Zbl 1185.47036
Hou, Jinchuan; Li, Chi-Kwong; Wong, Ngai-Ching
2010
Higher-rank numerical ranges and dilations. Zbl 1212.15022
Gau, Hwa-Long; Li, Chi-Kwong; Wu, Pei Yuan
2010
Numerical ranges of the powers of an operator. Zbl 1188.47006
Choi, Man-Duen; Li, Chi-Kwong
2010
Conditions for linear dependence of two operators. Zbl 1206.47005
Kuzma, Bojan; Lešnjak, Gorazd; Li, Chi-Kwong; Petek, Tatjana; Rodman, Leiba
2010
Operator radii and unitary operators. Zbl 1219.47012
Ando, Tsuyoshi; Li, Chi-Kwong
2010
Sum of Hermitian matrices with given eigenvalues: inertia, rank, and multiple eigenvalues. Zbl 1188.15039
Li, Chi-Kwong; Poon, Yiu-Tung
2010
Multiplicative maps preserving the higher rank numerical ranges and radii. Zbl 1193.15025
Clark, Sean; Li, Chi-Kwong; Sze, Nung-Sing
2010
Studying genetic code by a matrix approach. Zbl 1193.92037
Crowder, Tanner; Li, Chi-Kwong
2010
Preservers of eigenvalue inclusion sets. Zbl 1232.15021
Hartman, Jim; Herman, Aaron; Li, Chi-Kwong
2010
Euclidean and circum-Euclidean distance matrices: characterizations and linear preservers. Zbl 1211.51006
Li, Chi-Kwong; Milligan, Thomas; Trosset, Michael W.
2010
Maps preserving product $$XY -YX^*$$ on factor von Neumann algebras. Zbl 1183.47031
Cui, Jianlian; Li, Chi-Kwong
2009
Condition for the higher rank numerical range to be non-empty. Zbl 1172.15014
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2009
Preservers for norms of Lie product. Zbl 1181.15031
Li, Chi-Kwong; Poon, Edward; Sze, Nung-Sing
2009
The joint essential numerical range of operators: convexity and related results. Zbl 1178.47001
Li, Chi-Kwong; Poon, Yiu-Tung
2009
Spectrum, numerical range and Davis–Wielandt shell of a normal operator. Zbl 1167.47007
Li, Chi-Kwong; Poon, Yiu-Tung
2009
Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices. Zbl 1172.15003
Li, Chi-Kwong; Rodman, Leiba
2009
Linear preservers of higher rank numerical ranges and radii. Zbl 1200.15012
Clark, Sean; Li, Chi-Kwong; Mahle, Jennifer; Rodman, Leiba
2009
Graphs equienergetic with edge-deleted subgraphs. Zbl 1175.05087
Li, Chi-Kwong; So, Wasin
2009
Several products of distributions on manifolds. Zbl 1284.46033
Li, Chen Kuan
2009
Canonical forms, higher rank numerical ranges, totally isotropic subspaces, and matrix equations. Zbl 1152.15027
Li, Chi-Kwong; Sze, Nung-Sing
2008
Jordan isomorphisms and maps preserving spectra of certain operator products. Zbl 1134.47028
Hou, Jinchuan; Li, Chi-Kwong; Wong, Ngai-Ching
2008
Davis–Wielandt shells of operators. Zbl 1176.47010
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2008
Higher rank numerical ranges and low rank perturbations of quantum channels. Zbl 1151.47008
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2008
Polynomial numerical hulls of matrices. Zbl 1130.15017
Davis, Chandler; Li, Chi-Kwong; Salemi, Abbas
2008
Ranks and determinants of the sum of matrices from unitary orbits. Zbl 1137.15002
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2008
Schur multiplicative maps on matrices. Zbl 1147.15001
Clark, Sean; Li, Chi-Kwong; Rastogi, Ashwin
2008
Eigenvalues of the sum of matrices from unitary similarity orbits. Zbl 1167.15008
Li, Chi-Kwong; Poon, Yiu-Tung; Sze, Nung-Sing
2008
Spectral radius preservers of products of monnegative matrices. Zbl 1158.15002
Clark, Sean; Li, Chi-Kwong; Rodman, Leiba
2008
Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices. Zbl 1114.65034
Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong
2007
Mappings preserving spectra of products of matrices. Zbl 1113.15002
Chan, Jor-Ting; Li, Chi-Kwong; Sze, Nung-Sing
2007
Maps preserving the nilpotency of products of operators. Zbl 1124.47026
Li, Chi-Kwong; Šemrl, Peter; Sze, Nung-Sing
2007
$$G$$-invariant norms and bicircular projections. Zbl 1110.15025
Fošner, Maja; Ilišević, Dijana; Li, Chi-Kwong
2007
Mappings that preserve pairs of operators with zero triple Jordan product. Zbl 1130.15002
Dobovišek, M.; Kuzma, B.; Lešnjak, G.; Li, C. K.; Petek, T.
2007
$$C^*$$-isomorphisms, Jordan isomorphisms, and numerical range preserving maps. Zbl 1123.47032
Gau, Hwa-Long; Li, Chi-Kwong
2007
Extension of the total least square problem using general unitarily invariant norms. Zbl 1112.65037
Li, Chi-Kwong; Liu, Xin-Guo; Wang, Xue-Feng
2007
Schur product of matrices and numerical radius (range) preserving maps. Zbl 1121.15006
Li, Chi-Kwong; Poon, Edward
2007
Li, Chi-Kwong; Poon, Edward; Rastogi, Ashwin
2007
Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019
Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang
2007
Operators with numerical range in a given closed half plane. Zbl 1136.47004
Cheung, Wai-Shun; Li, Chi-Kwong; Rodman, Leiba
2007
...and 178 more Documents
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### Cited by 1,777 Authors

 161 Li, Chi-Kwong 43 Hou, Jinchuan 35 Lim, Yongdo 34 Nakazato, Hiroshi 34 Sze, Nung-Sing 32 Poon, Yiu-Tung 29 Chien, Mao-Ting 27 Bebiano, Natália Isabel Quadros 27 Tsing, Nam-Kiu 26 Psarrakos, Panayiotis J. 23 da Providência Santarém e Costa, João 23 Guterman, Alexander Èmilevich 22 Rodman, Leiba X. 21 Šemrl, Peter 21 Spitkovsky, Ilya Matvey 21 Taghavi Jelodar, Ali 19 Ma, Changfeng 19 Zhang, Xian 18 Bourhim, Abdellatif 17 Tam, Tin-Yau 17 Zhang, Guofeng 16 Cao, Yang 16 Lu, Fangyan 16 Yang, Aili 15 Wu, Yujiang 14 Gau, Hwa-Long 14 Lee, Hosoo 14 Molnár, Lajos 14 Zheng, Baodong 13 Fošner, Ajda 13 Ji, Guoxing 13 Poon, Edward 13 Wu, Peiyuan 12 Bai, Zhongzhi 12 Beasley, LeRoy B. 12 Chooi, Wai-Leong 12 Cui, Jianlian 12 Cushing, Jim M. 12 Kuzma, Bojan 12 Lou, Yuan 12 Moslehian, Mohammad Sal 12 Wong, Wing-Keung 11 Darvish, Vahid 11 Liang, Zhaozheng 11 Qi, Xiaofei 11 Wang, Kuo-Zhong 10 Bendaoud, Mohamed 10 Botelho, Fernanda 10 Cao, Chongguang 10 Kim, Sejong 10 Lau, Pan-Shun 10 Lawson, Jimmie Don 10 Lim, Ming-Huat 10 Mabrouk, Mohamed 10 Paul, Kallol 10 Petek, Tatjana 10 Salemi, Abbas 10 Wang, Xiang 10 Zheng, Qingqing 9 Chan, Jorting 9 Cheung, Waishun 9 Huang, Liping 9 Jamison, James Edward 9 Kribs, David W. 9 Maroulas, John 9 Massey, Pedro G. 9 Niezgoda, Marek 9 Song, Seok-Zun 9 van den Driessche, Pauline 9 Xu, Jinli 9 Yamazaki, Takeaki 9 Zhang, Fuzhen 9 Życzkowski, Karol 8 Bhatia, Rajendra 8 Chen, Fang 8 Cheng, Cheman 8 Coll, Carmen 8 Costara, Constantin 8 Fang, Xiaochun 8 Guo, Xueping 8 He, Kan 8 Ilišević, Dijana 8 Laurent, Monique 8 Lu, Linzhang 8 Pálfia, Miklós 8 Pereira Soares, Maria da Graca 8 Razeghi, Mehran 8 Sain, Debmalya 8 Sánchez, Elena 8 Seo, Yuki 8 Wang, Dengyin 8 Woerdeman, Hugo Jan 8 Wu, Shiliang 7 Choi, Man-Duen 7 Cosner, Chris 7 Duffner, Maria Antónia 7 El Abidine Abdelali, Zine 7 Iannazzo, Bruno 7 Li, Cuixia 7 Li, Xu ...and 1,677 more Authors
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### Cited in 285 Serials

 516 Linear Algebra and its Applications 279 Linear and Multilinear Algebra 65 Journal of Mathematical Analysis and Applications 51 Applied Mathematics and Computation 37 Journal of Computational and Applied Mathematics 30 Proceedings of the American Mathematical Society 28 Numerical Algorithms 27 Computers & Mathematics with Applications 25 SIAM Journal on Matrix Analysis and Applications 25 Operators and Matrices 21 Journal of Mathematical Biology 19 Journal of Functional Analysis 17 BIT 17 ELA. The Electronic Journal of Linear Algebra 16 Integral Equations and Operator Theory 14 Journal of Mathematical Physics 13 Positivity 13 Acta Mathematica Sinica. English Series 13 East Asian Journal on Applied Mathematics 12 Rocky Mountain Journal of Mathematics 12 Bulletin of the Iranian Mathematical Society 11 Computational and Applied Mathematics 11 Journal of Biological Dynamics 11 Banach Journal of Mathematical Analysis 10 Communications in Algebra 10 Journal of Mathematical Sciences (New York) 10 Annals of Functional Analysis 9 Bulletin of Mathematical Biology 9 Journal of Applied Mathematics and Computing 9 Advances in Operator Theory 8 Journal of Algebra 8 International Journal of Computer Mathematics 8 Numerical Linear Algebra with Applications 8 Complex Analysis and Operator Theory 7 Bulletin of the Australian Mathematical Society 7 Advances in Mathematics 7 Archiv der Mathematik 7 Journal of Algebraic Combinatorics 7 Journal of Difference Equations and Applications 7 Journal of Inequalities and Applications 7 Journal of the Australian Mathematical Society 7 Special Matrices 6 Discrete Mathematics 6 Mathematical Biosciences 6 Czechoslovak Mathematical Journal 6 Abstract and Applied Analysis 6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Quantum Information Processing 5 Studia Mathematica 5 Mathematische Annalen 5 Theoretical Population Biology 5 Applied Numerical Mathematics 5 Applied Mathematics Letters 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Asian-European Journal of Mathematics 5 Open Mathematics 4 International Journal of Theoretical Physics 4 Reports on Mathematical Physics 4 Rendiconti del Circolo Matemàtico di Palermo. Serie II 4 Transactions of the American Mathematical Society 4 European Journal of Operational Research 4 SIAM Journal on Applied Mathematics 4 Mathematical Programming. Series A. Series B 4 Finite Fields and their Applications 4 Advances in Computational Mathematics 4 Mediterranean Journal of Mathematics 4 Proyecciones 4 Journal of Theoretical Biology 3 American Mathematical Monthly 3 Discrete Applied Mathematics 3 Mathematics of Computation 3 Journal of Combinatorial Theory. Series A 3 Numerische Mathematik 3 European Journal of Combinatorics 3 Designs, Codes and Cryptography 3 Expositiones Mathematicae 3 SIAM Journal on Optimization 3 Advances in Applied Clifford Algebras 3 Filomat 3 The Electronic Journal of Combinatorics 3 Mathematical Problems in Engineering 3 Journal of Algebra and its Applications 3 Science China. Mathematics 3 Wavelets and Linear Algebra 2 Communications in Mathematical Physics 2 Letters in Mathematical Physics 2 The Mathematical Intelligencer 2 Annales de l’Institut Fourier 2 The Annals of Statistics 2 Calcolo 2 Canadian Journal of Mathematics 2 Canadian Mathematical Bulletin 2 Glasgow Mathematical Journal 2 Illinois Journal of Mathematics 2 Journal of Combinatorial Theory. Series B 2 Journal of Multivariate Analysis 2 Journal of Pure and Applied Algebra 2 Journal für die Reine und Angewandte Mathematik 2 Monatshefte für Mathematik 2 Quaestiones Mathematicae ...and 185 more Serials
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### Cited in 53 Fields

 1,026 Linear and multilinear algebra; matrix theory (15-XX) 615 Operator theory (47-XX) 305 Numerical analysis (65-XX) 216 Functional analysis (46-XX) 103 Quantum theory (81-XX) 102 Combinatorics (05-XX) 91 Biology and other natural sciences (92-XX) 47 Associative rings and algebras (16-XX) 47 Group theory and generalizations (20-XX) 41 Information and communication theory, circuits (94-XX) 36 Real functions (26-XX) 33 Operations research, mathematical programming (90-XX) 31 Partial differential equations (35-XX) 31 Convex and discrete geometry (52-XX) 28 Algebraic geometry (14-XX) 28 Dynamical systems and ergodic theory (37-XX) 28 Probability theory and stochastic processes (60-XX) 25 Nonassociative rings and algebras (17-XX) 24 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 24 Systems theory; control (93-XX) 23 Differential geometry (53-XX) 23 Statistics (62-XX) 20 Ordinary differential equations (34-XX) 18 Difference and functional equations (39-XX) 18 Geometry (51-XX) 15 Computer science (68-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 13 Topological groups, Lie groups (22-XX) 11 Fluid mechanics (76-XX) 10 Functions of a complex variable (30-XX) 9 Number theory (11-XX) 9 Global analysis, analysis on manifolds (58-XX) 8 Order, lattices, ordered algebraic structures (06-XX) 6 Approximations and expansions (41-XX) 6 General topology (54-XX) 5 History and biography (01-XX) 5 Integral equations (45-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Mechanics of particles and systems (70-XX) 3 General and overarching topics; collections (00-XX) 3 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Measure and integration (28-XX) 3 Special functions (33-XX) 3 Mechanics of deformable solids (74-XX) 2 Mathematical logic and foundations (03-XX) 2 Algebraic topology (55-XX) 2 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General algebraic systems (08-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX)