My main research direction is matrix algebra and its application in signal processing. I have published 60 SCI papers in top international journals such as Automatica, 5 papers in Automatica, 7 ESI highly cited papers, and 2 hot papers, including 30 SCI papers published in the past five years. Selected for the top 2% of global scientists and included in the Shanghai Oriental Talent Program (Youth Project). Won the second prize of the 2022 Shanghai Natural Science Award (second author), the second prize of the 2022 National Teaching Achievement Award (participant), and the first prize of the 2022 Shanghai Teaching Achievement Award (participant). Served as Secretary General of the Education Mathematics Professional Committee of the Chinese Association of Higher Education, Director of the Shanghai Mathematical Society, Editorial Board Member of the SCI journal Numerical Algorithms, Commentator of the American Mathematical Society Math. Review, and Reviewer for over 20 international SCI journals. Hosted research projects such as the National Natural Science Foundation of China General Program, Youth Program, Mathematics Tianyuan Special Fund, and Ministry of Science and Technology Foreign Experts Program, and led the municipal level first-class undergraduate course "Advanced Algebra" in Shanghai universities. I have been invited to visit and give presentations at renowned universities in the United States, France, South Korea, and other countries.
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.
1. Second Prize of Shanghai Natural Science Award in 2022 (second author)
2. Second Prize of National Teaching Achievement Award in 2022 (Participant)
3. First Prize of Shanghai Teaching Achievement Award in 2022 (Participant)
1. Top 2% of global scientists
2. 2023 Shanghai Oriental Talent Plan
1. Calculus
2. Linear Algebra
3. Higher Algebra
4. Probability Theory and Mathematical Statistics
5. Real Variable Functions
6. Matrix Theory
7. Mathematical Exploration and Discovery
1. Zhuo-Heng He, Li-Wei Ye, Yun-Ze Xu, Mei-Ling Deng, Qsvd method for arbitrary multiple sylvester-type coupled quaternion matrix equations with applications, Computational and Applied Mathematics, (2026), 45, 155.
2. Zhuo-Heng He, Yun-Ze Xu, Qing-Wen Wang, Xiang-Xiang Wang, Solving a system of quaternion matrix equations by using PSVD for multiple matrices with applications, Journal of Computational and Applied Mathematics, (2026), 476, 117072.
3. Chen-Yang Qi, Chang Liu, Zhuo-Heng He, Shao-Wen Yu, A Color Image Encryption Model Based on a System of Quaternion Matrix Equations, mathematics, (2026), 14, 319.
4. Zhuo-Heng He, Mei-Ling Deng, Jun-Jun Pan, Michael K. Ng, Diagonalization of two quaternion tensors with applications, Applied Mathematical Modelling, 148, 116278, (2025).
5. Jia-Wei Huo, Yun-Ze Xu, Zhuo-Heng He*, A simultaneous Decomposition for a quaternion Tensor Quaternity with Applications, mathematics, 13, 1679, (2025).
6. Zhuo-Heng He, Mei-Ling Deng, Shao-Wen Yu, T-Eigenvalues of Third-Order Quaternion Tensors, mathematics, (2025), 13, 1549.
7. Xin-Fang Zhang, Meng-Long Xiao, Zhuo-Heng He*, Orthogonal block Kaczmarz inner-iteration preconditioned flexible GMRES method for large-scale linear systems, Applied Mathematics Letters, Volume 166, article number 109529, (2025).
8. 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, 73 (7) 1269-1309 (2025).
9. 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).
10. 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).
11. 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.
12. 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).
13. Zhuo-Heng He, Jie Tian, Shao-Wen Yu, A system of four generalized Sylvester matrix equations over the quaternion algebra, mathematics, (2024), 12, 2341.
14. 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).
15. 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.
16. 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.
17. 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)
18. Zhuo-Heng He, Carmeliza Navasca, Xiang-Xiang Wang, Decomposition for a quaternion tensor triplet with applications, Advances in Applied Clifford Algebras, (2022) 32: 9.
19. 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.
20. 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).
21. 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.
22. 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.
23. Zhuo-Heng He, Some new results on a system of Sylvester-type quaternion matrix equations, Linear and Multilinear Algebra, 69 (16) (2021) 3069-3091.
24. 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.
25. 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.
26. 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.
27. 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.
28. Zhuo-Heng He, Meng Wang, A quaternion matrix equation with two different restrictions, Advances in Applied Clifford Algebras, (2021) 31: 25.
29. 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.
30. 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.
31. 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.
32. Xin Liu, Zhuo-Heng He*, On the split quaternion matrix equation AX = B, Banach Journal of Mathematical Analysis, 14, (2020) 228-248.
33. 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.
34. Zhuo-Heng He, Pure PSVD approach to Sylvester-type quaternion matrix equations, Electronic Journal of Linear Algebra, 35, (2019) 266-284.
35. Zhuo-Heng He, A system of coupled quaternion matrix equations with seven unknowns and its applications, Advances in Applied Clifford Algebras, (2019) 29: 38.
36. 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)
37. 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)
38. 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.
39. Zhuo-Heng He, Some quaternion matrix equations involving phi-Hermicity, Filomat, 33 (16) (2019) 5097-5112.
40. 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.
41. Qing-Wen Wang, Zhuo-Heng He, Yang Zhang, Constrained two-sided coupled Sylvester-type quaternion matrix equations, Automatica, 101 (2019) 207-213.
42. Zhuo-Heng He, Qing-Wen Wang, Yang Zhang, A system of quaternary coupled Sylvester-type real quaternion matrix equations, Automatica, 87 (2018) 25-31.
43. 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.
44. 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.
45. 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)
46. 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)
47. 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)
48. Qing-Wen Wang, Abdur Rehman, Zhuo-Heng He, Yang Zhang, Constraint generalized Sylvester matrix equations, Automatica, 69 (2016) 60-64.
49. 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.
50. Li Wang, Qing-Wen Wang, Zhuo-Heng He, The common solution of some matrix equations, Algebra Colloquium, 23 (2016) 71-81.
51. Zhuo-Heng He, Qing-Wen Wang, The general solutions to some systems of matrix equations, Linear and Multilinear Algebra, 63 (2015) 2017-2032.
52. 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.
53. Qing-Wen Wang, Zhuo-Heng He, Systems of coupled generalized Sylvester matrix equations, Automatica, 50 (2014) 2840-2844.
54. Qing-Wen Wang, Zhuo-Heng He, Solvability conditions and general solution for mixed Sylvester equations, Automatica, 49 (2013) 2713-2719.
55. 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.
56. Zhuo-Heng He, Qing-Wen Wang, The general solution to a coupled system of quaternion matrix equations, Linear and Multilinear Algebra, 61 (2013) 97-111.
