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On the Kronecker Products and Their Applications

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  • Huamin Zhang
  • Feng Ding

Abstract

This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vec-permutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of the Kronecker products.

Suggested Citation

  • Huamin Zhang & Feng Ding, 2013. "On the Kronecker Products and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, June.
    • Handle: RePEc:hin:jnljam:296185
    DOI: 10.1155/2013/296185
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    Cited by:

    1. Singh, Anup & Das, Subir & Ong, S.H., 2022. "Study and analysis of nonlinear (2+1)-dimensional solute transport equation in porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 491-500.
    2. Malik Zaka Ullah & Abdullah Khamis Alzahrani & Hashim Mohammed Alshehri & Stanford Shateyi, 2023. "Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance," Mathematics, MDPI, vol. 11(12), pages 1-12, June.
    3. Arnon Ploymukda & Pattrawut Chansangiam, 2016. "Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces," Journal of Mathematics, Hindawi, vol. 2016, pages 1-7, November.
    4. Alexander Dudin & Sergey Dudin & Rosanna Manzo & Luigi Rarità, 2022. "Analysis of Multi-Server Priority Queueing System with Hysteresis Strategy of Server Reservation and Retrials," Mathematics, MDPI, vol. 10(20), pages 1-19, October.
    5. Silva, Joeliton B. & de Albuquerque, Douglas F., 2022. "Tricritical behavior of the spin-3/2 anisotropic Heisenberg model with Dzyaloshinskii–Moriya interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    6. Srinivas R. Chakravarthy & Alexander N. Dudin & Sergey A. Dudin & Olga S. Dudina, 2023. "Queueing System with Potential for Recruiting Secondary Servers," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    7. Ampol Duangpan & Ratinan Boonklurb & Tawikan Treeyaprasert, 2019. "Finite Integration Method with Shifted Chebyshev Polynomials for Solving Time-Fractional Burgers’ Equations," Mathematics, MDPI, vol. 7(12), pages 1-24, December.
    8. Antonio Dalessandro & Gareth W. Peters, 2018. "Tensor Approximation of Generalized Correlated Diffusions and Functional Copula Operators," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 237-271, March.
    9. Bakhtiari, Mehrdad & Lakis, Aouni A. & Kerboua, Youcef, 2019. "Derivatives of fourth order Kronecker power systems with applications in nonlinear elasticity," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    10. Daniel A. Griffith, 2022. "Selected Payback Statistical Contributions to Matrix/Linear Algebra: Some Counterflowing Conceptualizations," Stats, MDPI, vol. 5(4), pages 1-16, November.

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