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de la Cruz, Ralph John

Professor
Email Addressrjdelacruz@math.upd.edu.ph
RoomMath Building 213
Websitevisit website (external)
Research Interests
Matrix Decompositions, Diagonalizability
Academic Groups
  • Teaching
    Mentoring
    PhD:
    DATU, NICOLE JOY, PADUA, “On Strongly ɸ-Reversible Elements of the Symplectic Group”
    MS:
    DOMINGO, KAE MARK, TIANSON, “On Trace Zero Symplectic Matrices”
    GALIMBA, ANGELO, VITUALLA, “On Nilpotent Quaternion Matrices”
    MISA, ELOISE, PEPITO, “The Algebra Generated by Nilpotent Elements in a Matrix Centralizer”
    ROBLES, BRYAN JOSEPH, MANIBOG, “On Sums of idempotents in a Matrix Centralizer”
    TAÑEDO, RAYMOND LOUIS, SARIOLA, “The Products of Involutions in a Matrix Centralizer”
    VILLEGAS, KERISH, SY, “On the Commutators of Real J-Symmetries”
    DE LARA, MARK LEXTER, TORRES,  “On the ɅRn-diagonalizability of Matrices in Cnxn”
    OLIVARIO, MARIA ISABEL, YU, ” On the Operator ф J and ζ J”
  • Publications
    • de la Cruz, R. J., Kennett Dela Rosa, & Angelo Galimba. Fillmore’s theorem and sums of nilpotent quaternion matrices.Electron. J. Linear Algebra 2025. DOI:10.13001/ela.2025.9089.
    • de la Cruz, R. J.,  Kerish Villegas. On the products of commutators of real $J$-symmetries. Electron. J. Linear Algebra 2025. DOI:10.13001/ela.2025.9041.
    • de la Cruz, R. J.,  William Nierop. Every 2n-by-2n complex symplectic matrix is a product of n + 1 symplectic dilatations. Linear Algebra Appl. 2025. DOI:10.1016/j.laa.2025.06.018.
    • de la Cruz, R. J.,  Kae Mark T. Domingo. On trace zero symplectic matrices. Linear Algebra Appl. 2025. DOI:10.1016/j.laa.2025.06.011.
    • de la Cruz, R. J. On the two-sided perplectic singular value decomposition and perplectically diagonalizable matrices.Asian-European J. Math. 2022. DOI:10.1142/S1793557122500474.
    • de la Cruz, R. J.,  Eloise Misa. The algebra generated by nilpotent elements in a matrix centralizer. Electron. J. Linear Algebra 2021. DOI:10.13001/ela.2022.6503.
    • de la Cruz, R. J.,  Philip Saltenberger. On the density of semisimple matrices in indefinite scalar product spaces.Electron. J. Linear Algebra 2021. DOI:10.13001/ela.2021.5509.
    • Afable, E. A., de la Cruz, R. J., Paras, A. T., & Segui, M. E. Diagonalizability with respect to perplectic and pseudo-unitary similarity transformations. Linear Algebra Appl. 2020. DOI:10.1016/j.laa.2020.01.010.
    • Awa, D.,  de la Cruz, R. J. Every real symplectic matrix is a product of real symplectic involutions. Linear Algebra Appl. 2020. DOI:10.1016/j.laa.2019.12.003.
    • de la Cruz, R. J.,  Darryl Q. Granario. Products of symplectic normal matrices. Linear Algebra Appl. 2018, 543, 162–172.
    • de la Cruz, R. J. Each 2n-by-2n complex symplectic matrix is a product of n + 1 commutators of J-symmetries. Linear Algebra Appl. 2017.
    • de la Cruz, R. J., Merino, D. I., & Paras, A. T. Every 2n-by-2n complex matrix is a sum of three symplectic matrices.Linear Algebra Appl. 2017.
    • de la Cruz, R. J., Merino, D. I., & Paras, A. T. Skew ϕ polar decompositions. Linear Algebra Appl. 2017.
    • De La Cruz, R. J., & Faßbender, H. On the diagonalizability of a matrix by a symplectic equivalence, similarity or congruence transformation. Linear Algebra Appl. 2016. DOI:10.1016/j.laa.2016.01.030.
    • de la Cruz, R. J., & Granario, D. Q. The φS polar decomposition when the cosquare of S is nonderogatory. Electron. J. Linear Algebra 2016. DOI:10.13001/1081-3810.3414.