Representation of sedenions multiplication via matrix-vector product

• Autorzy: Cariowa G. , Cariow A.
• Języki publikacji: EN

Abstrakty

EN

The article shows how to represent the multiplication of two sedenionss as a vector-matrix product. Matrfc, algebra offers not only a formalism for describing the algorithm, but it enables the derivation by pure algebraic manipulańons of an algorithm that is well suited to be implemented in vector and matrix digital data processors with various levels of paral-lelism. In addition, the mentioned procedures can be directly used for easy implementation in matrix-oriented languages like Matlab.

Słowa kluczowe

EN

Sedenions; multiplication of two sedenions; matrix notation

PL

sedenions; mnożenie dwóch sedenions; macierz notacji

• Wydawca: Komisja Informatyki Polskiej Akademii Nauk, Oddział w Gdańsku
• Czasopismo: Metody Informatyki Stosowanej
• Rocznik: 2011
• Tom: nr 1
• Strony: 133--139
• Opis fizyczny: Bibliogr. 20 poz., tab.

Twórcy

autor

Cariowa G.

autor

Cariow A.

• West Pomeranian University of Technology, Szczecin, Faculty of Computer Science and Information Technology

Bibliografia

• [1] Bülow T. and Sommer G., Hypercomplex signals - a novel extension of the analytic signal to the multidimensional case, IEEE Trans. Sign. Proc, vol. SP-49, no. 11, pp. 2844-2852, Nov. 2001.
• [2] Schiitte H.-D. and Wenzel J., Hypercomplex numbers in digital signal processing, in Proc. ISCAS '90, New Orleans, 1990, pp. 1557-1560.
• [3] Alfsmann D., On families of 2 N -dimensional hypercomplex algebras suitable for digital signal processing, in Proc. European Signal Processing Conf. (EUSIPCO 2006), Florence, Italy, 2006.
• [4] Alfsmann D., Gockler H. G., Sangwine S. J. and Eli T. A.. Hypercomplex Algebras in Digital Signal Processing: Benefits and Drawbacks (Tutorial). Proc. EURASIP 15th European Signal Processing Conference (EUSIPCO 2007), Poznań, Poland, 2007, pp. 1322-1326.
• [5] Sangwine S. J., Bihan N. Le, Hypercomplex analytic signals: extension of the analytic signal concept to complex signals, Proc. EURASIP 15th European Signal Processing Conference (EUSIPCO 2007), Poznań, Poland, 2007, Poznań, pp. 621-624.
• [6] Sangwine S. J., Fourier transforms of color images using ąuaternion or hypercomplex, numbers, in Electronics Letters, 10 Oct. 1996, vol. 32, pp. 1979-1980.
• [7] Sangwine S. J. and Eli T. A., Hypercomplex auto- and cross-correlation of color images, in Proc. ICIP, 1999, pp. 319-323.
• [8] Moxey C. E., Sangwine S. J., and Eli T. A., Hypercomplex correlation techniąues for vector images, IEEE Trans. Signal Processing, vol. 51, pp. 1941-1953, July 2003.
• [9] Ueda K. and S Takahashi. I., Digital filters with hypercomplex coefficients, in Proc. IEEE Int. Symp. Circuits Syst., May 1993, vol. 1, pp. 479-482.
• [10] Bayro-Corrochano E., Multi-resolution image analysis using the ąuaternion wavelet transform, Numerical Algorithms, Volume 39, Numbers 1-3, July, 2005, pp. 35-55.
• [11] Joao Luis Marins, Xiaoping Yun, Eric R. Bachmann, Robert B. McGhee, and Michael J. Zyda, „An Extended Kalman Filter for Quaternion-Based Orientation Estimation Using MARG Sensors", Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems Maui, Hawaii, USA, Oct. 29 - Nov. 03, 2001, pp. 2003-2011.
• [12] Ilias S. Kotsireas, Christos Koukouvinos, Orthogonal designs via computational algebra, Journal of Combinatorial Designs, 2006, v. 14, No 5, pp. 351-362,
• [13] Robert Calderbank , Sushanta Das, N. Al-Dhahir, And S. Diggavi, „Construction And Analysis Of A New Quaternionic Space-Time Code For 4 Transmit Antennas", Communications In Information And Systems, 2005, vol. 5, no. 1, pp. 97-122.
• [14] OZGUR ERTUG „Communication over Hypercomplex Kahler Manifolds: Capacity of Dual-Polarized Multidimensional-MIMO Channels", Wireless Personal Communications,2006, vol. 41, no 1, pp. 155-168.
• [15] Kevin Carmody, Circular and hyperbolic ąuaternions, octonions, and sedenions, Applied Mathematics and Computation, 1988, v. 28, Nol, pp. 47-72.
• [16] Kevin Carmody, Circular and hyperbolic quaternions, octonions, and sedenions - fur-ther results, Applied Mathematics and Computation, 1997, v. 84, No 1, pp. 27-47.
• [17] Imaeda, K.; Imaeda, M., Sedenions: algebra and analysis, Applied mathematics and computation, 2000,115 (2) pp. 77-88.
• [18] R. E. Cawagas. „On the structure and zero divisors of the Cayley-Dickson sedenion algebra". Discuss. Math. Gen. Algebra Appl., 24 (2004), 251-265.
• [19] Craig CULBERT, „Cayley-Dickson algebras and Loos", Journal of Generalized Lie Theory and Applications, Vol. 1 (2007), No. 1, pp. 1-17.
• [20] John C. Baez, „The Octonions", Bulletin Of The American Mathematical Society, 2001, v. 39, No 2, pp. 145-205.