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Simultaneous Diagonalization Under Weak Regularity and a Characterization

Author

Listed:
  • Fabián Flores-Bazán

    (Universidad de Concepción)

  • Felipe Opazo

    (Universidad de Concepción)

Abstract

We analyze the fulfillment of the simultaneous diagonalization (SD via congruence) property for any two real matrices, and develop sufficient conditions expressed in different way to those appeared in the last few years. These conditions are established under a different perspective, and in any case, they supplement and clarify other similar results published elsewhere. Following our point of view reflected in a previous work, we offer some necessary and sufficient conditions, different in nature to those in Jiang and Li (SIAM J Optim 26:1649–1668, 2016), for SD: roughly speaking our approach is more geometric and needs to compute images and kernels of matrices; whereas that in Jiang and Li (SIAM J Optim 26:1649–1668, 2016) requires to compute determinant and canonical forms. The bidimensional situation is particularly analyzed, providing new more precise characterizations than those in higher dimension and joint those given earlier by the authors. In addition, we also establish the connection of our characterization of SD with that provided in Jiang and Li (SIAM J Optim 26:1649–1668, 2016).

Suggested Citation

  • Fabián Flores-Bazán & Felipe Opazo, 2024. "Simultaneous Diagonalization Under Weak Regularity and a Characterization," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 629-650, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02526-y
    DOI: 10.1007/s10957-024-02526-y
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    References listed on IDEAS

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    1. Ting Pong & Henry Wolkowicz, 2014. "The generalized trust region subproblem," Computational Optimization and Applications, Springer, vol. 58(2), pages 273-322, June.
    2. Fabián Flores-Bazán & Giandomenico Mastroeni & Cristián Vera, 2019. "Proper or Weak Efficiency via Saddle Point Conditions in Cone-Constrained Nonconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 787-816, June.
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