A new approach to the concept of linearity. Some elements for a multiplicative linear algebra

References

• I. Barradas and J.E. Cohen, Iterated exponentiation, matrix-matrix exponentiation, and entropy, J. Math. Anal. Appl. 183(1) (1994), pp. 76–88. doi: 10.1006/jmaa.1994.1132
   Web of Science ®Google Scholar
• A.E. Bashirov, E.M. Kurpinar, and A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337(1) (2008), pp. 36–48. doi: 10.1016/j.jmaa.2007.03.081
   Web of Science ®Google Scholar
• M. Benzi, Preconditioning techniques for large linear systems: A survey, J. Comput. Phys. 182(2) (2002), pp. 418–477. doi: 10.1006/jcph.2002.7176
   Web of Science ®Google Scholar
• A.F. Cakmak and F. Basar, Some sequence spaces and matrix transformations in multiplicative sense, TWMS J. Pure Appl. Math. 6(1) (2015), pp. 27–37.
   Web of Science ®Google Scholar
• J.R. Cardoso and A. Sadeghi, On the conditioning of the matrix-matrix exponentiation, preprint (2017). Available at arXiv:1703.08804.
   Google Scholar
• F. Córdova-Lepe, The multiplicative derivative as a measure of elasticity in economics, TMAT Rev. Latinoam. Cienc. Ingr. 2(3) (2006).
   Google Scholar
• F. Córdova-Lepe and M. Pinto, From quotient operation toward a proportional calculus, Int. J. Math. Game Theory Algebra 18(6) (2009), pp. 527–536.
   Google Scholar
• F. Córdova-Lepe and M. Pinto, From quotient operation toward a proportional calculus, in Mathematics Research Perspectives, M.C. Leung, ed., Nova Science Publishers, New York, 2012, pp. 253–266.
   Google Scholar
• L. Florack and H. van Assen, Multiplicative calculus in biomedical image analysis, J. Math. Imaging. Vis. 42(1) (2012), pp. 64–75. doi: 10.1007/s10851-011-0275-1
   Web of Science ®Google Scholar
• M. Grossman and R. Katz, Non-Newtonian Calculus, Pingeon Cove, MA., Lee Press, 1972.
   Google Scholar
• U. Kadak and H. Efe, The construction of Hilbert spaces over the Non-Newtonian field, Int. J. Anal. 2014 (2014), Article ID 746059, 11 pages.
   Google Scholar
• U. Kadak and H. Efe, Matrix transformations between certain sequence spaces over the non-Newtonian complex field, Sci. World J. 2014 (2014), Article ID 705818, 12 pages.
   Google Scholar
• M. Mora, F. Córdova-Lepe, and R. Del-Valle, A non-Newtonian gradient for contour detection in images with multiplicative noise, Pattern. Recognit. Lett. 33(10) (2012), pp. 1245–1256. doi: 10.1016/j.patrec.2012.02.012
   Web of Science ®Google Scholar
• A. Ozyapici and B. Bilgehan, Finite product representation via multiplicative calculus and its applications to exponential signal processing, Numer. Algorithms 71(2) (2016), pp. 475–489. doi: 10.1007/s11075-015-0004-8
   Web of Science ®Google Scholar
• P. Perona, T. Shiota, and J. Malik, Anisotropic diffusion, in Geometry-driven Diffusion in Computer Vision, Haar Romeny, Bart M., ed., Springer, Netherlands, 1994, pp. 73–92.
   Google Scholar
• Y. Saad, Iterative Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics, Philadelphia, 2003.
   Google Scholar
• R. Terebes, M. Borda, C. Germain, R. Malutan, and I. Ilea, A multiplicative gradient-based anisotropic diffusion approach for speckle noise removal, in E-Health and Bioengineering Conference (EHB), 19–21 November, 2015, IEEE, Iasi, Romania, 2015, pp. 1–6.
   Google Scholar
• R. Terebes, M. Borda, R. Malutan, C. Germain, L. Bombrun, and I. Ilea, PolSAR image denoising using directional diffusion, in 2016 12th IEEE International Symposium on Electronics and Telecommunications (ISETC), 27–28 October, 2016, IEEE, Timisoara, Romania, 2016, pp. 339–342.
   Google Scholar
• J. Weickert, Anisotropic Diffusion in Image Processing, Vol. 1, Teubner, Stuttgart, 1998, pp. 59–60.
   Google Scholar
• N. Yalcin, E. Celik, and A. Gokdogan, Multiplicative Laplace transform and its applications, Optik Int. J. Light Electron Optics 127(20) (2016), pp. 9984–9995. doi: 10.1016/j.ijleo.2016.07.083
   Google Scholar
• Y. Zheng, Y. Zhou, H. Zhou, and X. Gong, Ultrasound image edge detection based on a novel multiplicative gradient and Canny operator, Ultrason. Imaging 37(3) (2015), pp. 238–250. doi: 10.1177/0161734614554461
   PubMed Web of Science ®Google Scholar