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2018 | 95 | 100-110
Article title

On the Moore-Penrose generalized inverse matrix

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Abstracts
EN
We analyze the compatibility of linear systems and the uniqueness of the corresponding solution via the singular value decomposition of an arbitrary n x m matrix. Our approach leads in natural manner to the Moore-Penrose’s generalized inverse between the subspaces of activation of the matrix under study.
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95
Pages
100-110
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References
  • [1] C. Lanczos, Am. Math. Monthly 65(9) (1958) 665-679.
  • [2] É. Picard, Rend. Circ. Mat. Palermo 25 (1910) 79-97.
  • [3] J. J. Sylvester, Compt. Rend. Acad. Sci. Paris 108 (1889) 651-653.
  • [4] C. Lanczos, Proc. Int. Congr. Math. Edinburgh-1958, Cambridge University Press (1960) 154-181.
  • [5] C. Lanczos, SIAM J. Appl. Math. 14(4) (1966) 831-863.
  • [6] C. Lanczos, Linear differential operators, Dover, New York (1997).
  • [7] F. Smithies, The Mathematical Gazette 47 (1963) 265-266.
  • [8] E. Schmidt, Teil 1, Mathematische Annalen Bd. 63 (1907) 433-476 and 64 (1907) 161-174.
  • [9] C. Jordan, J. de Mathématiques Pures et Appliquées, Deuxieme Série 19 (1874) 35-54.
  • [10] C. Jordan, Compt. Rend. Acad. Sci. Paris 78 (1874) 614-617.
  • [11] E. Beltrami, Giornale di Mathematische 11 (1873) 98-106.
  • [12] G. W. Stewart, SIAM Rev. 35 (1993) 551-566.
  • [13] J. J. Sylvester, Messenger of Mathematics 19 (1889) 42-46.
  • [14] L. Autonne, Compt. Rend. Acad. Sci. Paris 156 (1913) 858-860.
  • [15] E. T. Browne, Bull. Amer. Math. Soc. 36(10) (1930) 705-710.
  • [16] C. Eckart, G. Young, Bull. Amer. Math. Soc. 45(2) (1939) 118-121.
  • [17] H. Schwerdtfeger, Am. Math. Monthly 67(9) (1960) 855-860.
  • [18] I. J. Good, Technometrics 11(4) (1969) 823-831.
  • [19] C. Long, Mathematics Magazine 56(3) (1983) 161-167.
  • [20] S. J. Blank, N. Krikorian, D. Spring, Am. Math. Monthly 96(3) (1989) 238-239.
  • [21] D. Kalman, The College Mathematics Journal 27 (1996) 2-23.
  • [22] G. Golub, Johann Bernoulli Lecture, Univ. of Groningen, 8th April (1996).
  • [23] V. Gaftoi, J. López-Bonilla, G. Ovando, Current topics in quantum field theory research, Ed. O. Kovras, Nova Science Pub., New York, 2007, Chap. 10, 313-316.
  • [24] H. Yanai, K. Takeuchi, Y. Takane, Projection matrices, generalized inverse matrices, and singular, Springer, New York, 2011, Chap. 3.
  • [25] I. Guerrero-Moreno, J. López-Bonilla, L. Rosales-Roldán, The SciTech, J. Sci. & Tech. (India), Special Issue, Aug. (2012) 111-114.
  • [26] E. H. Moore, Bull. Am. Math. Soc. 26(9) (1920) 394-395.
  • [27] A. Bjerhammar, Trans. Roy. Inst. Tech. Stockholm 49 (1951) 1-86.
  • [28] R. Penrose, Proc. Camb. Phil. Soc. 51 (1955) 406-413.
  • [29] G. Nakos, D. Joyner, Linear algebra with applications, Brooks/Cole Pub., New York, 1998, Chap. 8.
  • [30] E. Weyr, C. R. Acad. Sci. Paris 100 (1885) 966-969.
  • [31] E. Weyr, Mon. für Mathematik und Physik 1 (1890) 163-236.
  • [32] T. N. E. Greville, SIAM Rev. 2(1) (1960) 15-22.
  • [33] G. H. Golub, W. Kahan, SIAM J. Numer. Anal. B2 (1965) 205-224.
  • [34] A. K. Hazra, Matrix algebra, calculus and generalized inverse, Cambridge Int. Sci. Pub. (2006).
  • [35] A. Ben-Israel, Electron. J. of Linear Algebra 9 (2002) 150-157.
  • [36] A. Ben-Israel, T. N. E. Greville, Generalized inverses: Theory and applications, Springer, New York, 2003.
  • [37] G. Green, An essay on the application of mathematical analysis to the theories of electricity and magnetism, (1828, private subscription, only fifty copies), reprinted in three parts at J. Reine Angewand. Math. 39 (1850) 73-89, 44 (1852) 356-374 and 47 (1854) 161-212.
  • [38] D. M. Cannell, George Green, mathematician & physicist 1793-1841, SIAM, Phil., USA (2001).
  • [39] A. Hernández-Galeana, J. López-Bonilla, J. Rivera-Rebolledo, Int. J. Math. Eng. Sci. 1(1) (2012) 8-12.
  • [40] P. Lam-Estrada, J. López-Bonilla, R. López-Vázquez, G. Ovando, Bull. of Kerala Mathematics Association 12(1) (2015) 43-52.
  • [41] H. C. Andrews, C. L. Patterson, Am. Math. Monthly 82 (1975) 1-13.
  • [42] C. B. Moler, D. Morrison, Am. Math. Monthly 90 (1983) 78-87.
  • [43] M. T. Heat, Scientific computing. An introductory survey, McGraw-Hill, New York (1997) Chap. 4.
Document Type
article
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YADDA identifier
bwmeta1.element.psjd-1f7fd979-e0de-467f-a770-c37270ca32d1
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