Hua-Lin Huang
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Hua-Lin Huang has a total of 27 co-authors. Here are the top co-authors by number of shared publications:
- Yu Ye
School of Mathematical Sciences University of Science and Technology of China(USTC)
10 shared publications - Huajun Lu
School of Mathematical Sciences, Huaqiao University, Quanzhou, People’s Republic of China
5 shared publications Lishan Fang
School of Mathematical Sciences, Huaqiao University, Quanzhou, China
5 shared publicationsYu Ye
5 shared publications- Chi Zhang
College of Sciences, Northeastern University, Shenyang 110004, China
4 shared publications - Yuping Yang
School of Mathematics and Statistics, Southwest University, Chongqing, China
4 shared publications
Latest Publications
- 21 August 2026
- Published by Elsevier in Journal of Symbolic Computation
- Vol. 139
Eigenvalues and equivalence classes of third-order symmetric tensors
- 21 August 2026
- Published by Elsevier in Journal of Symbolic Computation
- Vol. 139
Eigenvalues and equivalence classes of third-order symmetric tensors
- 20 February 2026
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 737, 193-212
Simultaneous block diagonalization of symmetric matrices via congruence
- 20 February 2026
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 737, 193-212
Simultaneous block diagonalization of symmetric matrices via congruence
- Open Access
Qi's problems on classifications of third- and fourth-order symmetric tensors by eigenvalues
This paper addresses two fundamental problems posed by Qi regarding the sufficiency of eigenvalues for the classification of symmetric tensors in the two-dimensional setting. For $2\times2\times2$ and $2\times2\times2\times2$ complex symmetric tensors, we establish their complete set of equivalence classes via a one-to-one correspondence with the canonical forms of their associated binary cubics and quartics. We then prove that these equivalence classes are uniquely determined by spectral invariants, specifically, the number of eigenpair classes and the multiplicities of zero eigenvalues, over the complex domain. We demonstrate that this classification does not hold in the real domain, where distinct equivalence classes can share identical spectral invariants. Finally, we extend this approach to derive canonical forms and complete classification for complex third- and fourth-order linear partial differential equations in two variables using their bijective relationship to binary forms.Open AccessQi's problems on classifications of third- and fourth-order symmetric tensors by eigenvalues
This paper addresses two fundamental problems posed by Qi regarding the sufficiency of eigenvalues for the classification of symmetric tensors in the two-dimensional setting. For $2\times2\times2$ and $2\times2\times2\times2$ complex symmetric tensors, we establish their complete set of equivalence classes via a one-to-one correspondence with the canonical forms of their associated binary cubics and quartics. We then prove that these equivalence classes are uniquely determined by spectral invariants, specifically, the number of eigenpair classes and the multiplicities of zero eigenvalues, over the complex domain. We demonstrate that this classification does not hold in the real domain, where distinct equivalence classes can share identical spectral invariants. Finally, we extend this approach to derive canonical forms and complete classification for complex third- and fourth-order linear partial differential equations in two variables using their bijective relationship to binary forms. - Open Access
Eigenvalues and equivalence classes of third-order symmetric tensors
This paper demonstrates that third-order real symmetric tensors cannot be classified up to equivalence by their eigenvalues only, thereby resolving a problem posed by Qi in 2006. By applying Harrison's center theory, we derive equivalence classes of $2 \times 2 \times 2$ symmetric tensors via the one-to-one correspondence with the canonical forms of their associated binary cubics. For such tensors, we compute the explicit characteristic polynomials and discover two previously unknown coefficients using the combination resultant. Pairs of third-order real symmetric tensors of all dimensions with identical eigenvalues but belonging to different equivalence classes are constructed to illustrate the inapplicability of eigenvalues for classification.Open AccessEigenvalues and equivalence classes of third-order symmetric tensors
This paper demonstrates that third-order real symmetric tensors cannot be classified up to equivalence by their eigenvalues only, thereby resolving a problem posed by Qi in 2006. By applying Harrison's center theory, we derive equivalence classes of $2 \times 2 \times 2$ symmetric tensors via the one-to-one correspondence with the canonical forms of their associated binary cubics. For such tensors, we compute the explicit characteristic polynomials and discover two previously unknown coefficients using the combination resultant. Pairs of third-order real symmetric tensors of all dimensions with identical eigenvalues but belonging to different equivalence classes are constructed to illustrate the inapplicability of eigenvalues for classification. - Open Access
The Waring Problem of Complex Binary Forms
The Waring problem of forms concerns the expression of homogeneous multivariate polynomials as sums of powers of linear forms. This paper focuses on complex binary forms, and we solve the Waring problem for them using basic tools in algebra and analysis. In particular, we present elementary treatments of the Apolarity Lemma and Sylvester's 1851 Theorem, which are easily accessible and will provide an ideal approach for future extension to the general case.
Open AccessThe Waring Problem of Complex Binary Forms
The Waring problem of forms concerns the expression of homogeneous multivariate polynomials as sums of powers of linear forms. This paper focuses on complex binary forms, and we solve the Waring problem for them using basic tools in algebra and analysis. In particular, we present elementary treatments of the Apolarity Lemma and Sylvester's 1851 Theorem, which are easily accessible and will provide an ideal approach for future extension to the general case.
- 2 July 2025
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 724, 320-335
Simultaneous direct sum decompositions of several multivariate polynomials
- 2 July 2025
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 724, 320-335
Simultaneous direct sum decompositions of several multivariate polynomials
- Open Access
- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in Electronic Research Archive
- Vol. 33 (9) , 5252-5276
Numerical algorithm and complexity analysis for diagonalization of multivariate homogeneous polynomials
We study the computational complexity of a diagonalization technique for multivariate homogeneous polynomials, expressing them as the sums of powers of independent linear forms. It is based on Harrison's center theory and consists of a criterion and a diagonalization algorithm. Detailed formulations and the computational complexity of each component of the technique are given. The complexity analysis focuses on the impacts of the number of variables and the degree of given polynomials. We show that this criterion runs in polynomial time, and the diagonalization process performs efficiently in numerical experiments. Other diagonalization techniques are reviewed and compared in terms of complexity.
- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in Electronic Research Archive
- Vol. 33 (9) , 5252-5276
Open AccessNumerical algorithm and complexity analysis for diagonalization of multivariate homogeneous polynomials
We study the computational complexity of a diagonalization technique for multivariate homogeneous polynomials, expressing them as the sums of powers of independent linear forms. It is based on Harrison's center theory and consists of a criterion and a diagonalization algorithm. Detailed formulations and the computational complexity of each component of the technique are given. The complexity analysis focuses on the impacts of the number of variables and the degree of given polynomials. We show that this criterion runs in polynomial time, and the diagonalization process performs efficiently in numerical experiments. Other diagonalization techniques are reviewed and compared in terms of complexity.
- 2 December 2024
- Published by Taylor & Francis in The American Mathematical Monthly
- Vol. 132 (3) , 218-236
Solving Algebraic Equations by Completing Powers
- 2 December 2024
- Published by Taylor & Francis in The American Mathematical Monthly
- Vol. 132 (3) , 218-236
Solving Algebraic Equations by Completing Powers
- Open Access
Solving cubic equations by completing the cube and higher degree equations by completing powers
We derive the Cardano formula of cubic equations by completing the cube, and provide radical solutions to some algebraic equations of higher degree by completing powers. The main idea of completing powers arises from Harrison's center theory of higher degree forms. A very simple criterion for such algebraic equations is presented, and the computation amounts to solving linear equations and quadratic equations.
Open AccessSolving cubic equations by completing the cube and higher degree equations by completing powers
We derive the Cardano formula of cubic equations by completing the cube, and provide radical solutions to some algebraic equations of higher degree by completing powers. The main idea of completing powers arises from Harrison's center theory of higher degree forms. A very simple criterion for such algebraic equations is presented, and the computation amounts to solving linear equations and quadratic equations.