Inverse Operation of Four-dimensional Vector Matrix

Full Text (PDF, 171KB), PP.19-27

Views: 0 Downloads: 0


H J Bao 1,* A J Sang 1 H X Chen 1

1. School of Communication Engineering, Jilin University, Changchun, China

* Corresponding author.


Received: 20 Jul. 2010 / Revised: 4 Dec. 2010 / Accepted: 25 Mar. 2011 / Published: 8 Aug. 2011

Index Terms

Multidimensional vector matrix, four-dimensional vector matrix determinant, four-dimensional vector matrix inverse


This is a new series of study to define and prove multidimensional vector matrix mathematics, which includes four-dimensional vector matrix determinant, four-dimensional vector matrix inverse and related properties. There are innovative concepts of multi-dimensional vector matrix mathematics created by authors with numerous applications in engineering, math, video conferencing, 3D TV, and other fields.

Cite This Paper

H J Bao, A J Sang, H X Chen, "Inverse Operation of Four-dimensional Vector Matrix", International Journal of Intelligent Systems and Applications(IJISA), vol.3, no.5, pp.19-27, 2011. DOI:10.5815/ijisa.2011.05.03


[1]Franklin, Joel L. [2000] Matrix Theory. Mineola, N.Y.: Dover.

[2]Ashu M.G. Solos. Multidimensional matrix mathematics: multidimensional matrix transpose, symmetry, ant symmetry, determinant, and inverse, part 4 of 6. Proceedings of the World Congress on Engineering 2010, vol.3, WEC 2010, June 30-July 2, 2010, London, U.K.

[3]Ahmed, N., Natarajan, T. and Rao, K. R. On image processing and a discrete cosine transform. IEEE Trans. Compute, l974, 23, 90–93.

[4]A J Sang, M S Chen, H X Chen, L L Liu and T N Sun. Multi-dimensional vector matrix theory and its application in color image coding. The Imaging Science Journal vol.58, no.3, June 2010, pp.171-176(6).

[5]Liu, L.L, Chen, H.X, Sang, A.J, Sun, T.N. “4D order-4 vector matrix DCT integer transform and its application in video code,” Imaging Science Journal, the vol. 58, no. 6, December 2010, pp.321-330 (10).

[6]I. Gessel and D. Stanton, Application of q-Lagrange inversion to basic hyper geometric series, Trans. Amer. Math. Soc. 277(1983), 173-203.

[7]Christian Krattenthaler and Michael Schlosser, “A New Multidimensional Matrix Inverse with Applications to Multiple q-series”, Discrete Mathematics, Volume 204, Issues 1-3, 6 June 1999, Pages 249-279.

[8]J. Riordan, Combinatorial identities, J. Wiley, New York, 1968.

[9]H.W. Gould, “A series transformation for finding convolution identities”, Duke Math.J.28 (1961), 193-202.

[10]H.W. Gould, “A new convolution formula and some new orthogonal relations for inversion of series”, Duke Math.J.29 (1962), 393-404.

[11]H.W. Gould, “A new series transform with application to Bessel, Legrende, and Tchebychev polynomials”, Duke Math. J. 31(1964), 325-334.

[12]H.W. Gould, “Inverse series relations and other expansions involving Humbert polynomials”, Duke Math.J.32 (1965), 691-711.

[13]H.W. Gould and L.C. Hsu, “Some new inverse series relations”, Duke Math.J.40 (1973), 885-891.

[14]G.E. Andrews, “Connection coefficient problems and partitions”, D. Ray- Chaudhuri, ed., Proc. Symp. Pure Math, vol.34, Amer. Math. Soc., Providence, R. I., 1979, 1-24.

[15]W.N. Bailey, “Some identities in combinatory analysis”, Proc. London Math. Soc. (2) 49 (1947), 421-435.

[16]W.N. Bailey, “Identities of the Roger-Ramanujan type”, Proc. London Math. Soc. (2) 50 (1949), 1-10.

[17]G. Gasper, “Summation, transformation and expansion formulas for bibasic series”, Trans. Amer. Soc. 312(1989), 257-278.

[18]M. Rahman, “Some quadratic and cubic summation formulas for basic hyper geometric series”, Can. J. Math. 45 (1993), 394-411.

[19]C. Krattenthaler, “A new matrix inverse”, Proc. Amer. Math. Soc. 124 (1996), 47-59.

[20]L. Carlitz, “Some inverse relations”, Duke Math. J. 40(1973), 893-901.