Journal of applied mathematics & informatics

  • 제42권5호
  • /
  • Pages.1155-1170
  • /
  • 2024
  • /
  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

A STUDY OF LINEAR MAPPING PRESERVING PYTHAGOREAN ORTHOGONALITY IN INNER PRODUCT SPACES

  • S. SYLVIANI (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran) ;
  • A. TRISKA (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran) ;
  • L. RATHOUR (Department of Mathematics, National Institute of Technology) ;
  • H. FULHAMDI (Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran) ;
  • D.A. KUSUMA (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran) ;
  • K. PARMIKANTI (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran) ;
  • F.C. PERMANA (Software Engineering Study Program, Kampus UPI di Cibiru)
  • 투고 : 2023.12.13
  • 심사 : 2024.07.09
  • 발행 : 2024.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The concept of orthogonality is widely used in various fields of study, both within and outside the scope of mathematics, especially algebra. The concept of orthogonality gives a picture of the relationship between two vectors that are perpendicular to each other, or the inner product in both of them is zero. However, the concept of orthogonality has undergone significant development. One of the developments is Pythagorean orthogonality. In this paper, it is explored topics related to Pythagorean orthogonality and linear mappings in inner product spaces. It is also examined how linear mappings preserve Pythagorean orthogonality and provides insights into how mathematical transformations affect geometric relationships. The results reveal several properties that apply to linear mappings preserving Pythagorean orthogonality.

키워드

과제정보

This research was funded by Hibah Riset Unpad Riset Data Pustaka Daring (RDPD) Universitas Padjadjaran grant number 1549/UN6.3.1/PT.00/2023.

참고문헌

  1. A.R. Gairola, A. Singh, L. Rathour, V.N. Mishra, Improved rate of approximation by modification of Baskakov operator, Operators and Matrices 16 (2022), 1097-1123. DOI: http://dx.doi.org/10.7153/oam-2022-16-72 
  2. A.R. Gairola, S. Maindola, L. Rathour, L.N. Mishra, V.N. Mishra, Better uniform approximation by new Bivariate Bernstein Operators, International Journal of Analysis and Applications 20 (2022), 1-19. DOI: https://doi.org/10.28924/2291-8639-20-2022-60 
  3. A.R. Gairola, N. Bisht, L. Rathour, L.N. Mishra, V.N. Mishra, Order of approximation by a new univariate Kantorovich Type Operator, International Journal of Analysis and Applications 21 (2023), 1-17. Article No. 106. DOI: https://doi.org/10.28924/2291-8639-21-2023-106 
  4. J. Alonso, H. Martini, S. Wu, (). On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces, Aequationes mathematicae 83 (2012), 153-189. 
  5. H. Anton, C. Rorres, A. Kaul, Elementary Linear Algebra, 12th ed, Wiley, New York, 2019. 
  6. L. Arambasic, R. Rajic, On Birkhoff-James and Roberts orthogonality, Special Matrices 6 (2018), 229-236. https://doi.org/10.1515/spma-2018-0018 
  7. L.J. Arambasic, R. Rajic, Roberts orthogonality for 2 * 2 2O 2 complex matrices, Acta Mathematica Hungarica 157 (2019), 220-228. 
  8. P.M. Bajracharya, B.P. Ojha, Birkhoff orthogonality and different particular cases of Carlsson's orthogonality on normed linear Spaces, Journal of Mathematics and Statistics 16 (2020), 133-141. 
  9. V. Balakrishnan, Mathematical physics: applications and problems, Springer Nature, 2020. 
  10. D. Bhattacharjee, An outlined tour of geometry and topology as perceived through physics and mathematics emphasizing geometrization, elliptization, uniformization, and projectivization for Thruston's 8-geometries covering Riemann over Teichmuller spaces, Authorea Preprints. 2022. 
  11. G. Birkhoff, & J. Von Neumann, The logic of quantum mechanics, The Logico-Algebraic Approach to Quantum Mechanics, Volume I, Historical Evolution, Dordrecht, Springer Netherlands, 1975, 1-26. 
  12. H. Chen, New MDS entanglement-assisted quantum codes from MDS Hermitian self-orthogonal codes, Designs, Codes and Cryptography, 91 (2023), 1-12. 
  13. J. Chmielinski, Linear mappings approximately preserving orthogonality, J. Math. Anal. Appl. 304 (2005), 158-169. 
  14. Deepmala, L.N. Mishra, V.N. Mishra, Trigonometric Approximation of Signals (Functions) belonging to the W(Lr, ξ(t)), (r ≥ 1)- class by (E, q) (q>0)-means of the conjugate series of its Fourier series, Global Journal of Mathematical Sciences (GJMS) 2 (2015), 61-69. 
  15. J. Dixmier, Sur la reduction des anneaux d'operateurs, In Annales scientifiques de l'Ecole normale suprieure 68 (1951), 185-202. 
  16. H.A. Dye, On the geometry of projections in certain operator algebras, Annals of Mathematics 61 (1955), 73-89. 
  17. B. Jacob, Linear Algebra, University of California, USA, 1990. 
  18. L.N. Mishra, M. Raiz, L. Rathour, V.N. Mishra, Tauberian theorems for weighted means of double sequences in intuitionistic fuzzy normed spaces, Yugoslav Journal of Operations Research 32 (2022), 377-388. DOI: https://doi.org/10.2298/YJOR210915005M 
  19. L.N. Mishra, V.N. Mishra, K. Khatri, Deepmala, On The Trigonometric approximation of signals belonging to generalized weighted Lipschitz W(Lr, ξ(t))(r ≥ 1)- class by matrix (C1 .Np
  20. G. Lumer, (). Semi-inner-product spaces, Transactions of the American Mathematical Society 100 (1961), 29-43. 
  21. H.A. Moon, T.J. Asaki, M.A. Snipes, Inner Product Spaces and Pseudo-Invertibility, In Application-Inspired Linear Algebra, Cham, Springer International Publishing, 2022, 379-477. 
  22. B.P. Ojha, P.M. Bajrayacharya, Relation of Pythagorean and Isosceles Orthogonality with Best approximations in Normed Linear Space, Mathematics Education Forum Chitwan 4 (2019), 72-78. https://doi.org/10.3126/mefc.v4i4.26360 
  23. C.C. Pugh, Real Mathematical Analysis, Cham, Springer International Publishing, 2015. 
  24. R. Sen, A First Course in Functional Analysis Theory and Applications, Athem Press, London, 2013. 
  25. S. Sylviani, E. Carnia, A.K. Supriatna, An algebraic study of the matrix meta-population model, In Journal of Physics: Conference Series 893 (2017), 012009. 
  26. S. Sylviani, H. Garminia, P. Astuti, Behavior for Time Invariant Finite Dimensional Discrete Linear Systems, Journal of Mathematical Fundamental Sciences 1 (2013). 
  27. S. Sylviani, H. Garminia, P. Astuti, Characterization of orthogonality preserving mappings in indefinite inner product spaces, Journal Mathematics and Computer Science 26 (2021), 10-15. 
  28. M.K. Sharma, N. Dhiman, Vandana, V.N. Mishra, Mediative Fuzzy Pythagorean Algorithm to Multi-criteria Decision-Making and Its Application in Medical Diagnostic, In: Ali, I., Chatterjee, P., Shaikh, A.A., Gupta, N., AlArjani, A. (eds) Computational Modelling in Industry 4.0. Springer, Singapore, 2022. https://doi.org/10.1007/978-981-16-7723-6 14 
  29. U. Uhlhorn, Representation of symmetry transformations in quantum mechanics, Arkiv Fysik 23 (1963), 307-341. 
  30. V.N. Mishra, L.N. Mishra, Trigonometric Approximation of Signals (Functions) in Lpnorm, International Journal of Contemporary Mathematical Sciences 7 (2012), 909-918. 
  31. V.N. Mishra, K. Khatri, L.N. Mishra, Deepmala; Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators, Journal of Inequalities and Applications 2013 (2013), 586. doi:10.1186/1029-242X-2013-586 
  32. V.N. Mishra, K. Khatri, L.N. Mishra; Statistical approximation by Kantorovich type Discrete q-Beta operators, Advances in Difference Equations 2013 (2013), 345. DOI: 10.1186/10.1186/1687-1847-2013-345 
  33. V.N. Mishra, T. Kumar, M.K. Sharma, L. Rathour, Pythagorean and fermatean fuzzy sub-group redefined in context of T-norm and S-conorm, Journal of Fuzzy Extension and Applications 4 (2023), 125-135. https://doi.org/10.22105/jfea.2023.396751.1262 
  34. V.N. Mishra, K. Khatri, L.N. Mishra, Deepmala, Trigonometric approximation of periodic Signals belonging to generalized weighted Lipschitz W' (Lr, ξ(t)), (r ≥ 1)- class by Norlund-Euler (N, pn)(E, q) operator of conjugate series of its Fourier series, Journal of Classical Analysis 5 (2014), 91-105. doi:10.7153/jca-05-08 
  35. V.N. Mishra, Some Problems on Approximations of Functions in Banach Spaces, Ph.D. Thesis, Indian Institute of Technology Roorkee 247 667, Uttarakhand, India, 2007. 
  36. V.N. Mishra, L.N. Mishra, Trigonometric Approximation of Signals (Functions) in Lpnorm, International Journal of Contemporary Mathematical Sciences 7 (2012), 909-918. 
  37. J.S. Lomont, & P. Mendelson, The Wigner unitarity-antiunitarity theorem, Annals of Mathematics 78 (1963), 548-559. 
  38. Z. Yang, Y. Li, A New Geometric Constant in Banach Spaces Related to the Isosceles Orthogonality, Kyungpook Mathematical Journal 62 (2022), 271-287. 
  39. A. Zamani, Approximately bisectrix-Orthogonality preserving mappings, Ferdowsi University of Mashhad, 2015. 
  40. Y. Zhao, M. Yu, S. Wu, C. He. An orthogonality type based on invariant inner products, Aequationes mathematicae 97 (2023), 707-724.