Zhuo-Heng He （何卓衡）
Professor, Department of Mathematics, Shanghai University, Shanghai, China
Vice dean of UTSEUS, Shanghai University, Shanghai, China
Academic employment
1. January, 2025—present, Full professor, Department of Mathematics, Shanghai University, China.
2. July, 2024—present, Vice dean of UTSEUS, Shanghai University, China.
3. March, 2020—December, 2024, Associate Professor, Department of Mathematics, Shanghai University, China.
4. May, 2018--February, 2020, Lecturer, Department of Mathematics, Shanghai University, China.
5. August, 2016--May, 2018, Visiting Assistant Professor, Department of Mathematics and Statistics, Auburn University, USA.
Education
1. September, 2013--June, 2016, Ph.D., Department of Mathematics, Shanghai University. Supervisor: Professor Qing-Wen Wang.
2. September, 2014 --September 2015: Joint Ph.D. student of KU Leuven, Department of Electrical Engineering STADIUS, Belgium. Supervisor: Professor Bart De Moor.
3. September, 2010--July, 2013: Master of Science, Department of Mathematics, Shanghai University. Supervisor: Professor Qing-Wen Wang.
4. September, 2006--July, 2010: Bachelor of Science, Department of Mathematics, Shanghai University.
Research Interests
1. Matrix theory over the quaternion algebra
2. Numerical Linear Algebra
3. Tensor theory over the quaternion algebra
Research Projects
1. 2019-2021, the National Natural Science Foundation of China, title: Some simultaneous decompositions of quaternion matrices and their applications. Project Director.
2. 2023-2026, the National Natural Science Foundation of China, title: The theory, algorithms and applications of some constrained quaternion matrix equations. Project Director.
3. January, 2023-December, 2023, the Ministry of Science and Technology of China, title: Some matrix decompositions and their applications in artificial intelligence. Project Director.
4. 2025-2025, the National Natural Science Foundation of China, title: Some systems of constrained Sylvester-type matrix equations over the quaternion algebra and their applications. Project Director.
Selected Published SCI Papers (2012-Present)
1. Zhuo-Heng He, Andrii Dmytryshyn, Qing-Wen Wang, A new system of sylvester-like matrix equations with arbitrary number of equations and unknowns over the quaternion algebra, Linear and Multilinear Algebra, https://doi.org/10.1080/03081087.2024.2413635
2. Lv-Ming Xie, Qing-Wen Wang, Zhuo-Heng He, The generalized hand-eye calibration matrix equation AX-YB = C over dual quaternions, Computational and Applied Mathematics, (2025), Volume 44, article number 137, (2025).
3. Zhuo-Heng He, Yun-Ze Xu, Qing-Wen Wang, Chong-Quan Zhang, The Equivalence canonical forms of two sets of five quaternion matrices with applications, Mathematical Methods in the Applied Sciences, (2025)
4. Zhuo-Heng He, Ting-Ting Liu, Xiang-Xiang Wang, Eigenvalues of quaternion tensors: properties, algorithms and applications, Advances in Applied Clifford Algebras, (2025) 35: 4.
5. Zhuo-Heng He, Wei-Lu Qin, Jie Tian, Xiang-Xiang Wang, Yang Zhang, A new Sylvester-type quaternion matrix equation model for color image data transmission, Computational and Applied Mathematics, (2024), Volume 43, article number 227, (2024).
6. Zhuo-Heng He, Jie Tian, Shao-Wen Yu, A system of four generalized Sylvester matrix equations over the quaternion algebra, mathematics, (2024), 12, 2341.
7. Chong-Quan Zhang, Qing-Wen Wang, Andrii Dmytryshyn, Zhuo-Heng He*, Investigation of some Sylvester-type quaternion matrix equations with multiple unknowns, Computational and Applied Mathematics, Volume 43, article number 181, (2024).
8. Chong-Quan Zhang, Qing-Wen Wang, Xiang-Xiang Wang, Zhuo-Heng He*, Restricted Singular Value Decomposition for a Tensor Triplet under T-Product and Its Applications, mathematics, (2024), 12, 982.
9. Zhuo-Heng He, Xiao-Na Zhang, Xiaojing Chen, Unitary Diagonalization of the Generalized Complementary Covariance Quaternion Matrices with Application in Signal Processing, mathematics, (2023), 11, 4840.
10. Zhuo-Heng He, Xiang-Xiang Wang, Yun-Fan Zhao, Eigenvalues of quaternion tensors with applications to color video processing, Journal of Scientific Computing, (2023) 94: 1. (ESI highly cited paper, Hot paper)
11. Zhuo-Heng He, Carmeliza Navasca, Xiang-Xiang Wang, Decomposition for a quaternion tensor triplet with applications, Advances in Applied Clifford Algebras, (2022) 32: 9.
12. Shao-Wen Yu, Xiao-Na Zhang, Wei-Lu Qin, Zhuo-Heng He, Some properties of the solution to a system of quaternion matrix equations, axioms, (2022) 11, 710.
13. Meng-Yan Xie, Qing-Wen Wang, Zhuo-Heng He, Mehany-Mahmoud Saad, A system of Sylvester-type quaternion matrix equations with ten variables, Acta Mathematica Sinica, English Series, (2022) https://doi.org/10.1007/s10114-022-9040-1
14. Zhuo-Heng He, Xiao-Na Zhang, Yun-Fan Zhao, Shao-Wen Yu, The solvability of a system of quaternion matrix equations involving Φ-skew-Hermicity, Symmetry, (2022) 14,1273.
15. Zhuo-Heng He, Jie Tian, Yun-Fan Zhao, Shao-Wen Yu, Consistency and general solutions to some Sylvester-like quaternion matrix equations, Symmetry, (2022) 14,1350.
16. Zhuo-Heng He, Some new results on a system of Sylvester-type quaternion matrix equations, Linear and Multilinear Algebra, 69 (16) (2021) 3069-3091.
17. Zhuo-Heng He, Meng Wang, Solvability conditions and general solutions to some quaternion matrix equations, Mathematical Methods in the Applied Sciences, 44 (18) (2021) 14274-14291.
18. Zhuo-Heng He, Wei-Lu Qin, Xiang-Xiang Wang, Some applications of a decomposition for five quaternion matrices in control system and color image processing, Computational and Applied Mathematics, (2021) 40, article no. 205.
19. Zhuo-Heng He, Michael K. Ng, Chao Zeng, Generalized singular value decompositions for tensors and their applications, Numerical Mathematics: Theory, Methods and Applications, 14 (3) (2021) 692-713.
20. Zhuo-Heng He, Chen Chen, Xiang-Xiang Wang, A simultaneous decomposition for three quaternion tensors with applications in color video signal processing, Analysis and Applications, 19 (3) (2021) 529-549.
21. Zhuo-Heng He, Meng Wang, A quaternion matrix equation with two different restrictions, Advances in Applied Clifford Algebras, (2021) 31: 25.
22. Shao-Wen Yu, Zhuo-Heng He*, Tian-Cheng Qi, Xiang-Xiang Wang, The equivalence canonical form of five quaternion matrices with applications to imaging and Sylvester-type equations, Journal of Computational and Applied Mathematics, 393 (2021) article no. 113494.
23. Shao-Wen Yu, Wei-Lu Qin, Zhuo-Heng He*, Some systems of tensor equations under T-Product and their applications, Filomat, 35 (2021) 3663-3677.
24. Zhuo-Heng He, Meng Wang, Xin Liu, On the general solutions to some systems of quaternion matrix equations, Rev. R. Acad. Cienc. Exactas F’is. Nat. Ser. AMat. RACSAM, (2020), 114:95.
25. Xin Liu, Zhuo-Heng He*, On the split quaternion matrix equation AX = B, Banach Journal of Mathematical Analysis, 14, (2020) 228-248.
26. Xin Liu, Zhuo-Heng He*, eta-Hermitian solution to a system of quaternion matrix equations, Bulletin of the Malaysian Mathematical Sciences Society, 43, (2020) 4007-4027.
27. Zhuo-Heng He, Pure PSVD approach to Sylvester-type quaternion matrix equations, Electronic Journal of Linear Algebra, 35, (2019) 266-284.
28. Zhuo-Heng He, A system of coupled quaternion matrix equations with seven unknowns and its applications, Advances in Applied Clifford Algebras, (2019) 29: 38.
29. Zhuo-Heng He, Qing-Wen Wang, Yang Zhang, A simultaneous decomposition for seven matrices with applications, Journal of Computational and Applied Mathematics, 349 (2019) 93-113. (ESI highly cited paper)
30. Zhuo-Heng He, Structure, properties and applications of some simultaneous decompositions for quaternion matrices involving phi-skew-hermicity, Advances in Applied Clifford Algebras (2019) 29: 6. (ESI highly cited paper)
31. Zhuo-Heng He, The general solution to a system of coupled Sylvester-type quaternion tensor equations involving eta-Hermicity, Bulletin of the Iranian Mathematical Society, 45 (2019) 1407-1430.
32. Zhuo-Heng He, Some quaternion matrix equations involving phi-Hermicity, Filomat, 33 (16) (2019) 5097-5112.
33. Xin Liu, Huajun Huang, Zhuo-Heng He*, Real representation approach to quaternion matrix equation involving phi-Hermicity, Mathematical Problems in Engineering, Article ID 3258349, 2019.
34. Qing-Wen Wang, Zhuo-Heng He, Yang Zhang, Constrained two-sided coupled Sylvester-type quaternion matrix equations, Automatica, 101 (2019)207-213.
35. Zhuo-Heng He, Qing-Wen Wang, Yang Zhang, A system of quaternary coupled Sylvester-type real quaternion matrix equations, Automatica, 87 (2018) 25-31.
36. Zhuo-Heng He, Qing-Wen Wang, Yang Zhang, The complete equivalence canonical form of four matrices over an arbitrary division ring, Linear and Multilinear Algebra, 66, (2018) 74-95.
37. Zhuo-Heng He, Jianzhen Liu, Tin-Yau Tam, The general phi-hermitian solution to mixed pairs of quaternion matrix Sylvester equations, Electronic Journal of Linear Algebra, 32, (2017) 475-499.
38. Zhuo-Heng He, Qing-Wen Wang, Yang Zhang, Simultaneous decomposition of quaternion matrices involving eta-Hermicity with applications, Applied Mathematics and Computation, 298 (2017) 13-25. (ESI highly cited paper)
39. Zhuo-Heng He, Qing-Wen Wang, A system of periodic discrete-time coupled Sylvester quaternion matrix equations, Algebra Colloquium, 24 (2017) 169-180. (ESI highly cited paper)
40. Zhuo-Heng He, Oscar Mauricio Agudelo, Qing-Wen Wang, Bart De Moor, Two sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices, Linear Algebra and its Applications, 496 (2016) 549-593. (ESI highly cited paper)
41. Qing-Wen Wang, Abdur Rehman, Zhuo-Heng He, Yang Zhang, Constraint generalized Sylvester matrix equations, Automatica, 69 (2016) 60-64.
42. F.O. Farid, Zhuo-Heng He, Qing-Wen Wang, The consistency and the exact solutions to a system of matrix equations, Linear and Multilinear Algebra, 64 (2016) 2133-2158.
43. Li Wang, Qing-Wen Wang, Zhuo-Heng He, The common solution of some matrix equations, Algebra Colloquium, 23 (2016) 71-81.
44. Zhuo-Heng He, Qing-Wen Wang, The general solutions to some systems of matrix equations, Linear and Multilinear Algebra, 63 (2015) 2017-2032.
45. Abdur Rehman, Qing-Wen Wang, Zhuo-Heng He, Solution to a system of real quaternion matrix equations encompassing eta-Hermicity, Applied Mathematics and Computation, 265 (2015) 945-957.
46. Qing-Wen Wang, Zhuo-Heng He, Systems of coupled generalized Sylvester matrix equations, Automatica, 50 (2014) 2840-2844.
47. Qing-Wen Wang, Zhuo-Heng He, Solvability conditions and general solution for mixed Sylvester equations, Automatica, 49 (2013) 2713-2719.
48. Zhuo-Heng He, Qing-Wen Wang, The eta-bihermitian solution to a system of real quaternion matrix equations, Linear and Multilinear Algebra, 62 (2013) 1509-1528.
49. Zhuo-Heng He, Qing-Wen Wang, A real quaternion matrix equation with applications, Linear and Multilinear Algebra, 61 (2013) 725-740. (ESI highly cited paper)
50. Qing-Wen Wang, Zhuo-Heng He, A system of matrix equations and its applications, Science China Mathematics, 56 (2013) 1795-1820.
51. Qing-Wen Wang, Xiang Zhang, Zhuo-Heng He, On the Hermitian structures of the solution to a pair of matrix equations, Linear and Multilinear Algebra, 61(2013) 73-90.
52. Zhuo-Heng He, Qing-Wen Wang, Solutions to optimization problems on ranks and inertias of a matrix function with applications, Applied Mathematics and Computation, 219 (2012) 2989-3001.
53. Qing-Wen Wang, Zhuo-Heng He, Some matrix equations with applications, Linear and Multilinear Algebra, 60 (2012) 1327-1353.
Invited Talk/ Colloquia
1. (Invited Talk) Some tensor decompositions over the quaternion algebra and their applications, SIAM Conference on Applied Linear Algebra, Sorbonne University, Paris, France, May 12-19, 2024.
2. (Invited Talk) Some tensor decompositions with applications, Workshop on Data Science and Scientific Computing, Hong Kong Baptist University, December 28-30, Hong Kong, China, 2023.
3. (Invited Talk) Some quaternion matrix equations with applications, Capital Normal University, April 19-21, Beijing, China, 2023.
4. (Colloquia) Some matrix equations and tensor decompositions over the quaternion algebra and their applications, Nankai University, June 16, 2022.
5. (Colloquia) Some matrix equations and tensor decompositions over the quaternion algebra and their applications, Fudan University, December 2, 2021.
6. (Invited Talk) 2021 China-Korea-USA International Conference on Matrix Theory, Hainan Normal University, China, November 26-27, 2021.
7. (Invited Talk) SIAM Conference on Applied Linear Algebra, New Orleans, May 17-21, 2021.
8. (Invited Talk) The 2021 Conference on Tensors, Hypergraphs and Their Applications, Suzhou University of Science and Technology, Suzhou, China, May 14-17, 2021.
9. (Invited Talk) The 8th International Conference on Matrix Analysis and Applications, University of Nevada, Reno, USA, July 15-18, 2019.
10. (Invited Talk) The 5th International Conference on Matrix Inequalities and Matrix Equations, Guilin University of Electronic Technology, Guilin, China, June 7-10, 2019.
11. (Invited Talk) International Conference on Matrix Theory and Applications: Combinatorics, Optimization, Data Analysis, Jeju University, Korea, May 23-27, 2019.
12. (Colloquia) Center of Mathematical Sciences, Zhejiang University, China, May 14, 2019.
13. (Invited Talk) 2019 Yangzhou Ring and Algebra conference, Yangzhou University, China, January 18-21, 2019.
14. (Invited Talk) 2018 China-Korea International Conference on Matrix Theory with Applications, Shanghai University, China, December 17-20, 2018.
15. (Colloquia) Department of Mathematics, Yangzhou University, China, June 12, 2018.
16. (Colloquia) Department of Mathematics, Taizhou University, China, June 11, 2018.
17. (Invited Talk) 2018 Southern Regional Algebra Conference, Auburn University at Montgomery , USA, April 20-22, 2018.
18. (Colloquia) Department of Mathematics, University of Alabama at Birmingham, Alabama, USA, April 6, 2018.
19. (Invited Talk) 2017 International Conference on Matrix Inequalities and Matrix Equations, Shanghai University, China, June 6-8, 2017.
20. (Invited Talk) Langenhop Lecture and SIU Mathematics Conference, Southern Illinois University, Carbondale, Illinois, USA, May 15-16 , 2017.
21. (Invited Talk) Southern Regional Algebra Conference 2017, University of South Alabama, Mobile, Alabama, USA, March 17-19, 2017.
Awards
1. The second prize of the National Teaching Achievement Award in 2023.
2. The first prize of the Shanghai Teaching Achievement Award in 2022.
3. The second prize of the Shanghai Natural Science Award in 2023.
4. The second prize of the Guangxi Natural Science Award in 2019.
5. Shanghai University Guanshen Cai Outstanding Young Teacher Awards, 2020.
6. Guo Benyu outstanding paper of young scholars, 2019.
I am a referee for the following organizations
Math Reviews.
Journal Editors
1. Associate Editor: Numerical Algorithms
I am a referee for the following international SCI journals
1. Advances in Applied Clifford Algebras.
2. Annals of Functional Analysis.
3. Applied Mathematics and Computation.
4. Applied Numerical Mathematics.
5. Automatica.
6. Bulletin of the Iranian Mathematical Society.
7. Computational and Applied Mathematics.
8. Electronic Journal of Linear Algebra.
9. Filomat.
10. IEEE Transaction on Signal Processing.
11. IET Control Theory and Applications.
12. Journal of Computational and Applied Mathematics.
13. Journal of the Franklin Institute.
14. Journal of Taibah University for Science.
15. Journal of Inequalities and Applications.
16. Linear Algebra and its Applications.
17. Linear and Multilinear Algebra.
18. Mathematical Methods in the Applied Sciences.
19. Mathematical Problems in Engineering.
20. Neurocomputing.
21. Operators and Matrices.
22. SIAM journal on Matrix Analysis and Applications.
23. Signal Processing.